Mr Cole-Hamilton called on all Scottish leaders to follow his party’s lead and pledge not to appear on Russian-state backed broadcasters.
It comes after Mr Salmond's pro-independence Alba Party criticised the UK and US for their “determined hyping” of the prospect of war in Ukraine.
Mr Cole-Hamilton said: “Being [Vladimir] Putin’s useful idiot may have stroked Alex Salmond’s ego and filled his bank account, but it’s an embarrassment to our nation that a former first minister could sink so low.
“If Alex Salmond had a shred of regard for human rights around the world, he should step aside and quit laundering the reputation of the Russian regime.”
He added: “Putin’s build-up of troops menacing Ukraine’s eastern border is an attempt to compel through force or threat its smaller neighbour to do as it wishes. That is a grave breach of international law.
“This is a dangerous escalation in Russian foreign policy and it should be called out.
“Here in the west, Putin’s propaganda broadcasters represent a powerful tool in his foreign policy arsenal for spreading confusion and disinformation.
"No representative of a Scottish party should be appearing on their channels.
"I hope that the other party leaders will join me in instructing their parliamentarians to reject Putin’s propagandists.”
Mr Salmond was approached for comment.