The distinction system gives consultants who already earn more than 100,000 annual top-ups of up to 75,000.
Distinction Awards are made over a number of years and can be linked to pensions, benefiting consultants into retirement.
The Deputy First Minister froze the budget for the awards scheme at 28 million last month and next year a further 2m will be shaved off.
Now, in a submission to a UK-wide review set up by Conservative Health Secretary Andrew Lansley, she has called for an alternative system to be set up.
She states: "It is increasingly difficult to defend a system that restricts access to rewards for exceptional contribution to one professional group only.
"Out of 162,000 staff working in NHS Scotland, only 3 per cent can access the distinction awards scheme."
The system proposed by Ms Sturgeon would see all NHS staff eligible for one-off bonuses.
A British Medical Association spokeswoman said: "Distinction awards are a means by which to promote excellence, quality, efficiency and innovation in the NHS in Scotland, all of which are key aims of the government.
"The awards help Scotland to not only keep the best doctors but attract the best from around the world."
Jackie Baillie, Scottish Labour's health spokeswoman, said: "If Nicola Sturgeon is serious about reforming the consultants' bonus scheme she should just get on and do it. This is a devolved matter and there is no need to wait for Westminster.
"In the current economic circumstances we need to see a much greater effort made to direct resources where they are needed most on the frontline."
A spokesman for Nicola Sturgeon said: "The Scottish Government is committed to … ensuring that key frontline services are delivered as efficiently and cost effectively as possible."