Open auditions had been scheduled to kick off Nov. 1 at New York's Apollo Theater. Instead, the process won't start until Nov. 22.
Hudson won an Oscar last year for her portrayal of ousted girl-group singer Effie White in the 2006 film adaptation of the Tony-winning musical.
"Our prayers and thoughts are with Ms. Hudson and her family at this tragic time," producer John Breglio said Monday.
"Due to this horrific tragedy, we feel this is not the time for a talent search for a role that is so closely connected with Ms. Hudson."
Hudson, whose mother, Darnell Donerson, and older brother, Jason Hudson, were found shot dead on Friday in Donerson's Chicago home. On Monday, it was confirmed that her 7-year-old nephew, who was reported missing Friday, had also been killed.