The motion passed 3-1 at a finance committee meeting on Nov. 26.
In November, the RCMP charged Fontana with fraud under $5,000, breach of trust by a public official and uttering forged documents.
The charges stem from allegations that Fontana inappropriately used federal government funds while a member of parliament to help cover the cost of his son's wedding reception.
Fontana, a former federal cabinet minister, has denied he did anything wrong. He is due to appear in court on Jan. 8 and has said he intends to plead not guilty.
He declared a conflict of interest at the Nov. 26 finance committee meeting and did not vote on the motion.
Under the Municipal Act, Fontana cannot be forced to resign by a council motion.