This is the second injury setback for Pakistan after batsman Sohaib Maqsood was also ruled out last week due to a fractured arm.
Read: Ruled out: Sohaib Maqsood out of Bangladesh tour with hand injury
Sohail, 31, suffered the injury on the last day of team's training session in Lahore after breaking down in his fourth over of a practise match.
Pakistan Cricket Board (PCB) said Sohail was advised to rest for two 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 release said.
Read: We are not going to take Bangladesh lightly: Azhar Ali
Sohail staged a surprise comeback after a four-year hiatus and impressed with his five-wicket in the key match against India in the World Cup held in Australia and New Zealand in February-March.
Pakistan chief selector Haroon Rashid has named Junaid as Sohail's replacement for the one-day squad.
Junaid was already part of the Twenty20 and Test squad for the Bangladesh series.
Pakistan will open the tour with the first of three one-day internationals in Dhaka on Friday. They also play a Twenty20 and two Tests on the tour.
Sohail is part of the Twenty20 and Test squad as well, but his place in these two formats is also doubtful after the latest injury setback.
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