As he stepped aside, Mr Applebaum told reporters that the charges against him were "unfounded".
He faces allegations of defrauding government, breach of trust and conspiracy, among others.
The city's first anglophone mayor in 100 years replaced Gerard Tremblay, who quit in November amid allegations related to illegal donations.
Mr Applebaum's arrest, in the early hours of Monday morning, is the latest in a string of scandals to hit Canadian local politics.
In the neighbouring province of Ontario, Toronto Mayor Rob Ford denies allegations that he appeared in a video smoking crack cocaine.
'Not a penny'
"Being mayor of Montreal is not something one can do while defending themselves against these accusations," Mr Applebaum said.
"This is why I am resigning as mayor of Montreal. It is a responsible thing to do."
He said he would "do everything I can to prove the accusations against me are unfounded".
"I have never taken a penny from anyone," he added.
Mr Applebaum began his term as interim mayor in November, vowing to fight corruption.
The charges against him stem from alleged acts before he became city mayor, during the years when he served as borough mayor, 2006-11.
Police officials offered few details, but said the charges related to real estate projects in Montreal.
Two officials with ties to Mr Applebaum's borough, Cote-des-Neiges-Notre-Dame-de-Grace, were also arrested by anti-corruption police on Monday.
Mr Applebaum had already said he had no plans to run in the mayoral election scheduled for November. Quebec officials and many city councillors have said the best option is for the city to select an interim mayor until then.
The allegations against Mr Tremblay came forward in an ongoing high-profile public inquiry in Quebec that uncovered links between the construction industry and organised crime.
In his statement on Tuesday, Mr Applebaum said he understood the frustration and cynicism of politics in the city.
"It is my deep conviction that I always acted in the best interest of all Montrealers," he said.