The English Premier League champions will play a second game against a Malaysia XI in Kuala Lumpur on Monday, having defeated the same team 3-2 in Saturday's opening match of the club's pre-season Asian tour.
United chief executive David Gill said the Indonesian government wanted the game in Jakarta to go ahead despite the bomb blasts killing at least nine people and injuring at least 50.
"The presidential office made a plea for us to go but, after discussions with the tour organizers and the Foreign Office, we decided it was not appropriate," Gill told the UK Press Association.
"We had to make a decision very quickly and it wasn't easy, but we feel this was the right one. We have a lot of talented footballers at Manchester United and we have to make sure they are safe, but that goes for everyone associated with the club.
"These situations are not easy but I am sure people will understand and one day we hope to go back."
United had earlier rejected an offer to play a match in Australia instead as it would have been too far to travel.
Meanwhile, new signing Michael Owen scored the winning goal on his debut after coming on as a second-half substitute against the Malaysia XI.
The England international, who joined on a free transfer from relegated Newcastle, pounced when the ball ran loose after Zoran Tosic went down in the penalty area.
United had taken a 2-0 first-half lead in front of almost 100,000 fans at the Bukit Jalil Stadium, with striker Wayne Rooney scoring the first and setting up the second for midfielder Nani.
Mohammed Amri Yahyah, one of only two full internationals to start for the home side, halved the deficit just before the interval and leveled eight minutes after the restart.
Veteran goalkeeper Edwin van der Sar was caught out of position for the first, and his second-half replacement Ben Foster made a hash of Darron Gibson's backpass to allow Yahyah and easy equalizer.
Owen horribly miscued a volleyed chance with his first touch after coming on, but clinically fired the winner with his next opportunity.
Manager Alex Ferguson was delighted with his new acquisition's performance.
"He's different from our other players, he's always searching for space, he's always in and around the box. He reacted well for his goal," Ferguson told reporters.
Owen was delighted to get off the mark in his first outing for United, having endured a miserable four years at Newcastle which saw him lose his international place.
"It's just nice to play with players who are on your wavelength, spotting your runs, and who are just class players," the 29-year-old said. "It's a nice feeling and it's nice to play a game in the red shirt.