David Watson, Scottish organiser at Unison Scotland, called for the Procurement Reform (Scotland) Bill to include minimum standards criteria to prevent companies that practice aggressive tax avoidance receiving public money.
The bill, which was discussed before a committee at Holyrood on Wednesday, is expected to be voted on later this year.
Holyrood should use the procurement bill to address aggressive tax avoidance rather than simply tax evasion, says Watson.
"The role of government is to make the big statement - we don't expect to be spending the public pound on companies that dodge tax.
"If you do that, it's a starting point. Then everybody else essentially comes into line," Watson told the Sunday Herald.
"Stopping tax dodging is a matter for the Treasury and governments across the world to do something about it - close down the tax havens, introduce global transparency laws.
"We can't do that alone in Scotland but procurement is one of the powers that we have got we can make it difficult for them."
The Scottish Government spends between £10 billion and £11bn a year, around one-third of its total budget, on expenditure that is not directly provided by public bodies - much of this money goes on public contracts with major private companies.
Watson said that some public bodies put out contracts to big private companies for about half a billion pounds a year, every year, in capital programme, adding: "There is huge sums of money involved for these firms.
"There is no public policy justification for Amazon not paying tax on every book that is sold from their Dunfermline or their Greenock distribution depot, that is self-evidently money generated in Scotland, handled in Scotland and just because they manage to find a way of routing the income because my PayPal or credit card bill goes via Luxembourg, that is self-evidently tax avoidance."
Such aggressive tax avoidance is damaging local, Scottish companies, says Watson.
"The Scottish Government's economy strategy is supposed to be about encouraging and developing Scottish companies, and they are at a disadvantage," he said.
"If you are a wee coffee shop competing with Starbucks, scale is already a challenge for you without them not paying taxes and you do. The Scottish Government ought to be concerned about that."
A Scottish Government spokesperson said: "Existing public procurement legislation already provides for the exclusion of companies that have failed to fulfil their legal obligations in respect of tax and social security.
"The Government has made clear that we intend to take the toughest line on tax avoidance.
"The Revenue Scotland and Tax Powers Bill which is currently before Parliament contains powers which will enable Revenue Scotland to take robust action to counteract tax avoidance in relation to devolved taxes.
"The Scottish General Anti-Avoidance Rule (GAAR) targets artificial tax avoidance arrangements and is both simpler and more comprehensive than the corresponding UK GAAR, which is based on a narrower test of 'abuse' rather than 'artificiality'."