He was due to be sentenced on Tuesday after he pleaded guilty in October to charges arising from a 2007 arrest when a gun was found on his tour bus.
The fire at the New York state court complex injured eight people. It is not clear when he will now be sentenced.
A February sentencing date was also postponed to allow the star — real name Dwayne Carter — to have dental work.
Carter faces up to a year in prison after he admitted attempted criminal possession of a weapon in a plea deal.
His lawyer, Stacey Richman, said he was unhappy about the postponement because he was braced to start his sentence.
“Once you make up your mind to do something, you want to do it,” she said.
The sentencing could be rescheduled for Wednesday if the court buildings are in a fit state to reopen.
About 1 000 people were evacuated from the buildings during the fire.
Earlier this week, Carter, 27, told MTV he had already shot seven music videos in one night ahead of his sentence. — BBCOnline.