Mish Rahman, who sits on the party’s NEC ruling body, accused Mr Navalny of being a “far right racist” over a 2007 video where he compared Muslims in Chechnya to “cockroaches”.
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Mr Rahman criticised Sir Keir for praising the “courage” of the activist, who died in a Russian prison on Friday.
He wrote on X: “A case of my enemy’s enemy is my friend.
“Ignoring the fact that Navalny was a far right Nazi sympathiser.
“Starmer’s ignorance has no bounds.”
Tory MP Bob Seely said: “This looks like more evidence that the Labour Party hasn’t changed.
“Directly below Labour’s leadership its senior activists appear to be attacking pro-Western democrats rather than its adversaries.”
The Sun on Sunday understands Mr Rahman’s comments do not pass the threshold to face disciplinary action.
He declined to comment but said: “Navalny’s Islamophobic record is plain to see.”
Labour has suspended two parliamentary candidates over anti-Israel comments.