The Red Sox were due to play the Kansas City Royals in a Major League Baseball game at Fenway Park, while the Bruins were down to host the Pittsburgh Penguins in the National Hockey League at TD Garden.
"Tonight's Red Sox game at Fenway Park has been postponed to support efforts of law enforcement officers," the Rex Sox announced on their Twitter account.
"We're going to do like everybody else," Royals manager Ned Yost said. "We're just waiting it out and seeing what happens.
"They're not opening the ballpark right now until the situation is resolved."
There was no immediate decision on when the Red Sox would reorganise their game but the NHL tentatively rescheduled the Bruins-Penguins game to Saturday afternoon.
The Penguins were supposed to play Buffalo on Saturday night but that game was moved to April 23.
It was the second time this week that the Bruins rescheduled a game. They were due to play the Ottawa Senators on Monday but moved it to April 28 after the bombing earlier in the day that killed three people and injured 176.
The Boston Celtics and Indiana Pacers also had their National Basketball Association game on Tuesday cancelled.
The game was not rescheduled because the result would have had no impact on the seedings for the NBA play-offs, starting Saturday. The Celtics will open their postseason against the New York Knicks at Madison Square Garden.
Saturday's National Women's Soccer League game in Boston was also rescheduled while the New York Red Bulls announced they would honour the Boston marathon victims before Saturday's game against New England Revolution.
The father-in-law of New England goalkeeper Matt Reis was seriously injured in Monday's blasts.
The normally traffic-clogged streets of Boston were eerily quiet on Friday as the search for an ethnic Chechen suspected in the bombings intensified.
Public transport was suspended, air space was restricted and famous universities, including Harvard and MIT, were closed after police ordered residents to remain at home.
"It's pretty scary," Royals reliever Tim Collins said.
"I've never been part of anything like this and, obviously, there are tons of people affected by it but you just have to wait and, hopefully, they get the guy."
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