Baisya suffered an ankle injury during Bangladesh's Super Eights defeat against Australia in Antigua last week.
"The reports indicated Baisya will require six to eight weeks of rehabilitation before he regains full fitness so the (World Cup) technical committee has approved Reza as replacement," said an International Cricket Council statement.
The 20-year-old Reza, who has played 12 one-day internationals, is the eighth replacement player to be called up for the tournament so far.
Pakistan replaced Abdul Razzaq, Shoaib Akhtar and Mohammad Asif, while New Zealand brought in replacements for Daryl Tuffey and Lou Vincent -- who both suffered injuries during the tournament.
Australia had to replace spearhead Brett Lee, who suffered an ankle injury before the World Cup started.
England were Thursday allowed to replace their paceman Jon Lewis with quick bowler Stuart Broad.