Finance Secretary John Swinney has said an independent Scotland "will continue to have a lottery and lottery infrastructure".
Conservative MSP Nanette Milne wrote to National Lottery operator Camelot asking if it had been approached by SNP ministers and was told that the future of the lottery in Scotland is not a matter for them but for the respective governments to decide.
Ms Milne is calling for an assurance that an independent Scotland would still have a share of the billions of pounds of lottery good causes funding, particularly as the independence campaign is being heavily funded by Euromillions winners Chris and Colin Weir.
In a letter to Ms Milne, Camelot head of policy and public affairs Richard Hickson wrote: "Any decisions about the future shape of the National Lottery following a Scottish vote for independence in the referendum would be a matter for the respective governments, not Camelot.
"This also applies to the arrangements in place of distributing funds to National Lottery good causes.
"To date, National Lottery players have raised over £29 billion for the good causes with more than 400,000 individual awards made across the UK, an average of 128 lottery grants for every postcode district.
"We have not had any meetings with SNP ministers on this matter to date."
Ms Milne said: "John Swinney said only a few months ago that he had discussions about keeping the Lottery under independence. Yet, neither he nor any of his ministerial colleagues have even bothered to meet with the very people running the UK National Lottery.
"The SNP and the Yes campaign are being bankrolled by lottery winners but they have no idea whether the people of Scotland will still get the chance to play the lottery. Communities and the country's sporting stars will also be wondering if they will continue to benefit from the billion given out from the lottery's good causes fund.
"The UK National Lottery has been vital to funding the training success of Scottish Olympic and Paralympic sportsmen and women with our athletes winning 13 of Team GB's 65 medals at the London Olympics.
"And for many small retailers, sales from UK National Lottery tickets are vital to their business turnover so any loss of revenue could have a big impact on their business."
A spokeswoman for Mr Swinney said: "An independent Scotland will continue to have a lottery and lottery infrastructure, and the current Camelot contract runs to 2023.
"People across Scotland have invested significant amounts through the national lottery and any suggestion from Westminster that they would seek to take Scotland's lottery cash would be a significant blow to the No campaign.
"As Camelot, the National Lottery operator, makes clear, it is for the two governments to agree exact arrangements, which is why the Tory-led Government should agree to discussions ahead of the referendum, a position supported by over two-thirds of people in Scotland.
"However, given that Scotland already contributes to the lottery, there is absolutely no reason why it should not continue to operate as it does just now.
"As the Scottish Government continues to build the case for independence to be put to voters in a referendum next year we will engage in discussions across a wide range of issues including the funding of charities and good causes."