The seamer will be replaced by Junaid Khan for the series which starts with an ODI on Friday in Dhaka.
Sohail, 31, suffered the injury after breaking down in his fourth over of a practise match in Lahore.
This is the second injury setback for Pakistan after batsman Sohaib Maqsood was ruled out last week due to a fractured arm.
The Pakistan Cricket Board (PCB) said Sohail was advised to rest for up to three weeks.
“Sohail suffered a back injury at the training camp, precisely reporting pain during the practice match, and post MRI scan he was advised recuperation for 2-3 weeks,” a PCB statement said.
Sohail had impressed in the World Cup campaign after a four-year absence from the side.
Pakistan will open the tour with three one-day internationals followed by a Twenty20 and two Tests against the Tigers.