"It is simply not appropriate to go forward with a political debate when a disaster strikes. The focus for all of us before, during and after the storm needs to be on emergency response and disaster relief, not campaigns and politics," he said.
Warren's campaign manager Mindy Meyers agreed in a statement released by the campaign on Monday evening.
"Elizabeth believes the focus now must be on public safety and ensuring people get the help they need during the storm and in its aftermath," she said.
"With the concern for public safety and cleanup paramount, Elizabeth believes the debate should not be held tomorrow."
Brown has spent much of the day at emergency response shelters and in meetings with local and state authorities planning storm preparation and response. He and Warren both canceled their campaign events on Monday, but as of Monday afternoon, the PBS affiliate hosting the debate, WGBH, had planned to continue with the debate as scheduled.
The storm is causing cancellations of presidential and Senate campaign activities up and down the East Coast, with both Mitt Romney and President Obama taking time off from the trail to allow local authorities to focus on storm response. At least one other Senate debate, in Maine, originally scheduled for Tuesday night, has been moved to Friday.
--This story was updated at 6:49 p.m.