The gaffe came after the two hosts of the BBC One Breakfast show asked the 67-year-old singer how he kept in such good shape.
"Well, I don't know, running is good - unless you're in the Boston Marathon," the seventies superstar said, before adding the words "terrible, terrible".
Startled, the presenters scrambled to continue.
Outraged viewers around the world turned to Twitter to share their opinion.
User @Pontussengstrom called the comment "truly insensitive" while @glennalli referred to it as "an awful joke".
Meanwhile, @lassevacklen was even less impressed.
"Bad taste. Bad timing. Bad joke," he wrote.
The bomb blasts killed at least three people and left more than 150 people injured.
The Abba front man was in the UK to promote his newest song, We Write the Story, which he co-wrote with former Abba band mate Benny Andersson as well as Stockholm DJ Avicii. The song will be performed at the opening of the Eurovision Final in Malmö on May 18th.
Later on Tuesday, Ulvaeus apologized for his comments.
“This morning on BBC Breakfast I let my tongue slip with terrible results," he said in a statement.
He explained that the comment was not meant to be a joke but that he quickly realized it could be interpreted as such.
"I feel very, very bad about it, I am truly sorry and I hope that everybody understands that it was an unbelievably stupid slip of the tongue.
"As everyone else I feel sorrow about what's happened and deep compassion with the victims of this atrocity."
See full interview here, the Boston comments come after 1.25