The former first minister said the Scottish Government he led "would not have turned its back" on this "badly neglected" group of workers.
He said: "But the mistakes of the past must not be repeated. Time is of the essence. They need support in the coming days, not weeks and not months."
Mr Salmond, who leads the pro-independence Alba Party, said taxi drivers were essential workers "every bit as much as bus drivers and railway staff".
He said: "However, unlike other small businesses they have received very little compensation for loss of earnings and such support as they have received from councils has been patchy and in some cases derisory, with many private hire and taxi drivers forced out of business altogether.
“Private hire and taxi drivers have been the poor relations during the pandemic receiving little or no support.
"It is assumed that because they do not have premises, that private hire and taxi drivers do not have the same costs, but they have significant overheads without the business rates and other reliefs available to other small businesses.
"With new restrictions coming into force hitting the hospitality and nightlife economy this has had a devastating effect on the incomes of these essential workers.
“It is now imperative that the Scottish Government steps in to support these essential workers."
Murray Fleming, general secretary of the Scottish Taxi Federation, said the sector was facing an "ongoing battle to survive".
He said it relied heavily on hospitality during the festive season and had seen a "massive downturn" at what would normally be a busy time.
Mr Fleming said: "We will be lobbying the Government, along with other trade bodies, to get some form of financial support."
However, Mr Fleming said he was "not overly optimistic".
A Scottish Government spokesman said: "We are all too aware of the impact that Covid-19 has had – and continues to have – on business and the Scottish economy.
"The emergence of the new Omicron variant and the speed at which it is spreading brings even more economic uncertainty.
“That is why the actions we have taken so far, including the latest £375 million package of financial support recently announced by the First Minister, are firmly focused on supporting businesses, protecting jobs and mitigating the continuing impact of Covid on our wider economy.
“The Scottish Government is acutely aware of the financial implications for many businesses and we are working at pace with business sectors and industry to develop targeted financial support for businesses that will be impacted by the restrictions, including those required to close.”