Baisya suffered the injury while bowling in Bangladesh's 10-wicket defeat by Australia on Saturday but could still play a part in the tournament.
"The x-ray report shows no fracture and the physio will try to get him fit for the game against South Africa," he added.
Bangladesh play South Africa in Guyana on April 7.
Skipper Habibul Bashar said left-arm seamer Syed Rasel will replace him for the New Zealand match.
Bangladesh, playing in their third World Cup, are featuring in the second round for the first time.
