In a letter, Mr Davey pointed out that gas supply profit margins at some suppliers were several times higher than margins on electricity.
Analysis alongside the letter suggested the former nationalised company may be benefiting from a "strong monopoly position".
He said that reducing the rate of earnings from gas to the level on electricity could save consumers nearly £40 a year.
The Cabinet minister's fresh intervention in the energy debate knocked £600 million off the value of British Gas parent Centrica as shares fell by nearly 4% though they later pared back some of the losses. Rival SSE fell as much as 2%.
Mr Davey was accused of sparking a "witch hunt" against energy firms and of threatening jobs.
The minister wrote to regulator Ofgem, which is investigating the market alongside other bodies.
He said: "I want them to think radically. It is an independent process. They could decide to take no action or they could decide to go for a full-scale market investigation.
"There could be a number of remedies if they go down that route, including the breaking up of some of these companies if they have been shown to abuse their market power."
Figures accompanying his letter to Ofgem chief executive showed British Gas has 41% of the market share in gas, and generated a profit margin of 11.2% in 2012 on domestic supply.
"It is clear that the former monopoly gas supplier British Gas has retained a very substantial market share," analysis alongside the data said.
"Does this indicate that British Gas has a strong monopoly position which enables it to generate high profit margins?"
The figures showed the average margin for gas supply across the so-called Big Six suppliers - including SSE, E.ON, EDF, npower and Scottish Power as well as British Gas - was 6.7% in 2012.
SSE's margin, at 11.4%, was higher than that of British Gas - though its market share, at 12%, was lower.
Margins on domestic electricity supply across the industry were an average 1.8%, according to the data.
Energy prices have been high on the political agenda after a pledge by Labour to cap bills should it win the next election.
But Mr Davey told Today that debate and analysis had been focused on dual fuel bills including electricity rather than focusing on gas "where the figures are suggesting there is a bigger problem".
"If profits on gas supply were brought in line with those made on electricity supply, that could mean savings of nearly £40 off the average annual bill, so this is a significant number for consumers out there who are struggling with energy bills."
The double digit margins from British Gas and SSE on gas supply contrast with the 5% figure for overall domestic energy, which has been cited by both companies amid the debate prompted by higher bills.
SSE chief executive Alistair Phillips-Davies said in a blog last year: "Most people think that is a reasonable amount to make. Indeed, it's a smaller margin than most food retailers."
But the margins on gas of above 11% are much higher than those of Tesco and Sainsbury's which in 2013 annual results posted levels of 5.3% and 3.6%.
In his letter, Mr Davey said there was evidence British Gas had tended "to charge one of the highest prices over the past three years, and has been on average the most profitable".
He wrote: "Clearly you will wish to consider whether this is prima facie evidence of an issue in the market and so whether it merits a market investigation reference with the whole gamut of potential remedies that could follow."
British Gas said it was complying with an ongoing independent market assessment being conducted by the Office of Fair Trading (OFT), Ofgem and the Competition & Markets Authority (CMA).
"The data referred to in the Secretary of State's letter has already been fully disclosed and in the public domain for a number of months," a spokeswoman said.
Labour accused the Government of letting energy suppliers get away with increasing their profits on the back of spiralling bills.
Ofgem said it would look at all evidence while compiling its report with the CMA and OFT. It declined to comment further.
Gary Smith, national officer of the GMB union, accused Mr Davey of unleashing a "hugely damaging feeding frenzy" on British Gas, a company which employs tens of thousands of workers in this country when other jobs in the sector are being exported to low wage countries by foreign-owned firms.
"British Gas is probably the biggest employer of apprentices and trainees in the UK.
"Hundreds of apprenticeships in smart metering that would have been created this year probably won't be because of Davey's dithering over policy. He now threatens to wreck thousands of more jobs.
"If an investigation is warranted it should have been carried out appropriately not by a ministerial leak to the press leading to a witch hunt."
John Allan, national chairman of the Federation of Small Businesses, welcomed Mr Davey's intervention.
He said: "Over 40% of all small businesses are with British Gas and it simply cannot be right that one company has such a dominant share, especially given the price of gas now accounts for between five to 10 per cent of total business costs for nearly one in 10 of the UK's smallest businesses.
"The business energy market is in desperate need of reform and we want to see radical measures put in place to increase transparency in the market and allow small firms to switch to more competitive energy deals with ease."
British Gas director Chris Weston defended the company's record and said it welcomed "a proper, thorough and independent examination of the issues".
He added: "Britain has one of the most competitive energy markets in the world, with gas and electricity prices among the lowest in western Europe. Around 80% of British Gas customers have switched their tariff or supplier at least once.
"About two thirds of British Gas customers are dual fuel customers, taking both gas and electricity, and the price of the gas is the same for all customers whether they are a gas-only customer or on a dual fuel tariff. British Gas' profit margins are on average 5% after tax.
"Our parent company Centrica does more than any other organisation to secure gas and power for British customers, with commitments totalling more than £60 billion, and we can only shoulder responsibilities on this scale if we are a profitable business.
"In the last six years we have invested £13.7 billion, which is equivalent to £1.85 for every £1 earned. We also support jobs and growth in Britain, directly employing more than 30,000 people. Our annual tax bill is around £1 billion, making us one of Britain's biggest corporate tax-payers.
"The current assessment of the energy market will be essential to rebuilding trust in the sector. We strongly support a proper, thorough and independent examination of the issues during this process."