Andy Bell's name will remain on the ballot paper for the election of the new Denny and Banknock councillor.
However, a Labour spokesman said the party had "withdrawn its support".
The Daily Record newspaper reported that Mr Bell had made anti-Catholic remarks on Facebook.
The by-election, taking place on Thursday, was called after SNP ward councillor John McNally was elected MP for Falkirk at May's general election.
A statement from Scottish Labour said: "Andy Bell has been suspended by the Labour Party pending an investigation.
"Although it is too late for Mr Bell to be removed from the ballot, the party has withdrawn any support for him as a by-election candidate."
A Labour candidate standing in a Falkirk Council by-election has been suspended pending an investigation over sectarian comments he was said to have made on social media.