It comes after Bradley appeared in court on allegations he assaulted and harassed his wife. The judge ordered Bradley to attend anti-violence therapy and to stay away from his wife.
Five of the seven council members said the charges against Bradley had become too much of a distraction for a city facing a fiscal crisis.
White Plains is facing a potential 18 percent property tax increase in the new budget year.
The council does not have the power to remove the 48-year-old Democrat.
He is facing misdemeanor charges, and refused to yield to council's call he should step down as mayor.
Bradley said at a news conference on Monday evening that he deserved the "right to due process" as any other citizen. He said his fellow elected officials were rushing to judgment.
Court papers filed last Thursday allege that Bradley told his wife that she should recant her charges against him or go to a mental hospital and say she was crazy.
Fumiko Bradley had accused her husband of slamming a door on her hand, resulting in his Feb. 28 arrest on an assault charge.
On March 5, she announced she did not want him prosecuted and would not cooperate. According to the court papers, that is about the time Adam Bradley told her she should recant the charge.
The mayor has pleaded not guilty.