The US band, who had been due to play in the Indonesian capital next weekend, issued a statement apologising to fans, reported E! Online.
"We... Hope one day we can make it up to them," continued the statement posted on the Facebook page of concert promoter Ismaya Live.
Concert promoters scrapped the nearly sold-out gig out of precaution after police arrested two suspected militants and confiscated bombs that the duo were allegedly looking to set off against the Myanmar Embassy in the Indonesian capital.
Police in Indonesia had refused to issue a permit for the US pop star after Islamic groups objected to her show, claiming it was too vulgar.
More From This Section
They had called upon the singer to tone down her performance but her management took the decision to pull the plug instead.
Fellow pop star Rihanna twice pulled out of concerts in the city in 2008 and 2009.
Singer Steven Tyler arrived in Manila on Sunday, where the band are due to play as part of their ongoing world tour.