Mr Salmond, who has presented the ‘Alex Salmond Show’ on the channel since 2017, said there was “no productive point” in having the future of the show “dominate Prime Minister’s Questions”.
The former SNP leader had faced mounting pressure to disassociate himself from RT, formerly Russia Today, following the invasion of Ukraine by the Kremlin.
The decision to suspend the show also comes after former Liberal Democrat leader Sir Vince Cable’s appeared on the programme on Thursday morning, a decision labelled “entirely wrong” by the party’s Scottish leader.
In a statement, Mr Salmond called the condemnation of opposition politicians of his show “blatant attacks on freedom of speech”, and claimed it had “whipped up a crescendo of personal abuse” towards former SNP MP Tasmina Ahmed-Sheikh, who jointly runs the production company behind the programme.
He said: “We now have the worst of all fears – a hot war in Europe. The efforts of every single person should be to re-establish the peace.
"That certainly is our focus, and therefore Slàinte Media have decided to suspend the Alex Salmond Show until that can be secured.
"There is no productive point in having the future of a television show dominate Prime Minister’s Questions as it did yesterday, when politicians should be rising to the occasion of the great issues of peace in Europe.”
He defended the more than 200 episodes of the show, claiming there has not been a “single piece of editorial interference of any kind from RT”.
Mr Salmond added: “In contrast, the blatant attacks on freedom of speech from establishment political parties are not just entirely hypocritical, but have whipped up a crescendo of personal abuse and harassment of my co-presenter Ms Ahmed-Sheikh to the extent that she is now quite legitimately concerned about the safety of her family.
"All wars come to an end. Let us pray that this one will not escalate even further. Now every single persons’ efforts should turn to supporting attempts to regain the peace.”
The statement came after Sir Vince Cable, who was business secretary during the Cameron/Clegg coalition government and who led the Lib Dems between 2017 and 2019, appeared on the show on Thursday.
The show was pulled from the main schedule of RT, formerly Russia Today, but is available in full on the website.
Sir Vince told The Scotsman he has asked RT not to broadcast the interview in light of the full-blown invasion of Ukraine.
He said: “The interview had nothing to do with the situation in Ukraine and was about the paperback version of my book, Money and Power, and my earlier novel.
“I totally condemn the invasion and fully support Nato sanctions and the position of [existing party leader] Ed Davey that British measures should be strengthened.
“In view of this morning’s events I have asked RT not to broadcast the interview.”
Alex Cole-Hamilton, the leader of the Scottish Liberal Democrats, labelled the appearance “entirely wrong”.
He said: "Vince Cable is a private citizen and no longer a LibDem parliamentarian, but his appearance on Salmond’s RT show this morning was entirely wrong. So too is Salmond’s continued association with this agent of a hostile power.
"No elected Scottish Liberal Democrat will appear on RT."
Nicola Sturgeon said on Wednesday she was “appalled” by her former mentor’s ongoing involvement with the channel, adding she had previously warned against the move.
She said: “I don’t think it’s any secret now that I didn’t think he should ever have had a television show on RT.
“But it is even more unthinkable now that that should continue.”