The Alba Party leader spoke out after William had private discussions with former Labour prime minister Gordon Brown during his recent visit to Scotland.
Mr Brown played a key role in the successful campaign to keep Scotland in the Union in 2014 – which saw the Queen urging voters north of the border to “think very carefully” on the issue ahead of the referendum.
Mr Salmond, who was first minister when the vote on Scotland’s place in the UK took place in 2014, accused pro-UK leaders of “unscrupulous unionist desperation” by trying to recruit the royals to campaign for the Union.
And he insisted it showed “poor judgment on both sides” for William to meet Mr Brown.
The former SNP leader said: “Whatever Prince William thought he was doing by agreeing to a confab with Gordon Brown just as he set up his latest campaign for the union … We should have no hesitation in seeing from that meeting, unionist preparation for attempting to persuade a constitutional monarchy to intervene in a constitutional debate which should be left to the people.”
The leader of the Alba Party, which failed to win any seats in the recent Holyrood election, insisted: “It would be very wise for the royal family to follow what has been the Queen’s example over her long reign, to keep the monarchy over and above politics, and it would be foolish to have a situation in which it can be said that the monarchy is involved in the Scottish Constitutional debate.”
He added: “Back in 2014, David Cameron made a last-ditch desperate and failed attempt to drag the Queen into politics. The Brown meeting shows poor judgment on both sides, but the same degree of unscrupulous unionist desperation. The independence team should take note.”
With Holyrood having a majority of independence supporting MSPs, Mr Salmond insisted that the case for Scottish independence must now be progressed “as a matter of urgency”.
The Alba Party leader said: “It is quite clear that the forces of the Union, David Cameron previously, and now Gordon Brown, have no compunction in getting themselves ready and set for what is coming in the next referendum campaign.
“However, the Scottish Parliament elections have left them in a state of disarray. That is why the case for Scottish independence must be progressed now as a matter of urgency. The Tories at Westminster are surprised that they are not already facing a renewed constitutional challenge and are wondering what on earth is going on.”
“It would be infinitely better for the independence side to seize the moment and strike when the iron is hot to progress the constitutional issue.
“Alba’s membership continues to rise as we press for the case for Scottish independence to be progressed with urgency and democratic determination.”