The former Formula One world champion spoke out amid renewed calls for the race later this month to be called off for a second year running.
It came as relatives and supporters of a jailed anti-Bahrani Government activist feared he was seriously ill after he went on hunger strike more than 60 days ago, and seven police were injured by a bomb blast.
With security tight, the 12 teams are thought to be on the brink of pulling out of the event and the Grand Prix ringmaster Bernie Ecclestone is understood to have said the decision is up to them.
Speaking from Switzerland, Sir Jackie told The Herald: "I strongly believe it shouldn't be cancelled and the reason for that is much broader than purely F1 or even Bahrain.
"We have been fighting for democracy for a great many years and I certainly am a supporter of that, but democracy cannot be done in one week, one month, one year. It's impossible, as we've seen."
Last year's race was cancelled after more than 40 people died, many after being tortured, following Shia-led protests against the Sunni ruling family.
The race, which is due to be held on Sunday, April 22, has been shrouded in controversy due to the continued clashes.
Former world champion Damon Hill has called for the race to be cancelled.
MPs voiced worries at the weekend in the wake of fresh protests and the growing concern for the condition of the jailed activist Abdulhadi Alkhawaja who has been on hunger strike.
However, Sir Jackie said cancellation "would be more damaging to the rest of the world".
He added: "If a peaceful demonstration were to take place it would be much more positive for their movement to a desired democracy.
"The Grand Prix is the most televised sports event in the world. It is therefore a very powerful message."
He added: "You've got to be very careful because if you were to say the Bahrain Grand Prix should not take place then will there be pressure on Russia, for example, for the Winter Olympics when they come round in 2014? Will there be demonstrations because Russia is still trying to create democracy? It's ironic there will be a meeting taking place in China this week on whether to go to Bahrain.
"I truly believe that if you take the religious issue out of it for a moment, that Bahrain is more advanced in the democratic movement than any other country in the Middle East right now, but because of the religious issue it has become more disruptive."
Sir Jackie said that religious tensions should not mean sporting events cannot take place, adding: "You've got to be very careful. If this race is cancelled then I think it is a very backward position to have in sport.
"We have already got a model in Northern Ireland where football continued to be played and so did rugby and so did motorcycling."
Sir Jackie, who won the Formula One world championship three times, goes further than those who say sporting events should remain neutral. He insists they can play an active, positive role, adding: "Sport is a positive force, it brings people together."
He fears cancelling the race would create more problems.
"It's the loss to the economy, because if they lose the grand prix this year, they may never get it back," he said.
"It's between £300m and £500m we're talking about.
"In Bahrain, the taxi drivers, hoteliers, waiter – all of those people employed – will suffer because there is no grand prix taking place.
"They will suffer more because of that than the issue of stopping the grand prix because there has been not enough movement towards democracy in a 12-month period, which will create more unrest and unhappiness."
Mr Ecclestone said: "We've no way we can force people to go there. We're not involved in any of the politics in Bahrain, over who is right or wrong."
On Monday, anti-Government computer hackers disrupted the website of Bahrain's national airline Gulf Air, the grand prix's main sponsor, in protest.
A group calling itself February 14 Defence posted photos and videos of their message of boycotting the racing event.