Applebaum's resignation came just seven months after he took office.
Former Mayor Gerald Tremblay also left office because of a scandal, The Globe and Mail reported Tuesday.
Police arrested Applebaum Monday on charges including fraud toward the government, breach of trust, conspiracy and municipal corruption.
He is among the latest of Quebec officials investigated on allegations that public-works contracts were being inappropriately given by municipalities to well-connected firms.
In his announcement, Applebaum reasserted his innocence, saying he's "never taken a penny from anybody."
"I would like to tell Montrealers that I love them," he said, adding that he understood their feelings of frustration and disappointment.
The resignation means the city's 62-member City Council must elect a successor to be mayor until Nov. 3 elections, The Globe and Mail reported.
The council will likely vote on Applebaum's replacement as early as next week.