The tentative plan for the Bruins is to play their scheduled game against Pittsburgh on Saturday afternoon at 12:30 p.m. ET. The NHL will make a final decision by 8:30 a.m. ET.
The rescheduling would mean that Pittsburgh's originally planned home game against Buffalo, to have taken place on Saturday evening, would occur instead on Tuesday.
Authorities had shut down the metropolitan area's transit system and advised people to not venture out until further notice.
The Bruins had already been forced to move a game after Monday's bombing at the famed Boston Marathon led to the deaths of three people. About 170 more people were injured, included several who needed amputations.
That scheduled contest with the Ottawa Senators, which will likely help determine Eastern Conference playoff matchups, was moved to April 28, making it the NHL's final regular-season game and the only one scheduled for that day.
The Bruins had been set to put playoff tickets up for sale Friday morning, but that has been moved to Monday.
The Sox were scheduled to open a home series at Fenway Park against Kansas City. There was no immediate word as to when it would now take place.
Players from both clubs and their staff were told to stay away from the park until an official decision had been made.
"We've been told not to go outside. We've been told the hotel has been locked down, although I've seen a handful of people moving around," Royals vice-president Mike Swanson said. "The streets are just, wow. It's numbingly quiet for a noon hour in Boston."
The NBA earlier this week cancelled a late-season game between the Boston Celtics and Indiana Pacers, as it did not affect the final season standings. The Celtics have their NBA playoff opener Saturday against the Knicks at Madison Square Garden in New York.
The New England Patriots postponed for the second time a news conference with director of player personnel Nick Caserio about next week's NFL draft. The news conference originally had been scheduled for Tuesday but was postponed after the bombings. It has been rescheduled for Monday.