The injury to the 22-year-old is a major blow to Pakistan's chances in the six-nation Asia Cup starting in the United Arab Emirates from August 27.
Shaheen's injury has already forced him to miss the second Test in Sri Lanka last month.
The left-armer has accompanied the team to the Netherlands for a three-match one-day international series and was in rehabilitation before doctors advised him to rest for four to six weeks.
"Shaheen has been advised 4-6 weeks rest by the PCB Medical Advisory Committee and independent specialists following latest scans and reports," said a Pakistan Cricket Board (PCB) release.
Doctors hope the paceman will return to competitive cricket in October with the T20 international tri-series in New Zealand, which will be followed by the ICC Men's T20 World Cup Australia 2022.
Shaheen anchored Pakistan's upset win over India in last year's Twenty20 World Cup, also played in the UAE.
A PCB medical officer said he is expected to recover with rest.
"I have spoken with Shaheen and he is understandably upset with the news, but he is a brave young man who has vowed to come back strongly to serve his country and team," doctor Najeebullah Soomro is quoted as saying in the release.
"Shaheen will stay with the squad to complete his rehabilitation and his replacement for the Asia Cup will be announced shortly," the release added.
The Pakistan side will arrive in Dubai from Rotterdam on Monday.
Shaheen has so far played 25 Tests, 32 one-day internationals and 40 T20 internationals in a career that has ascended in the last three years.
He was declared men's cricketer of the year in 2021 after taking 78 wickets in 36 internationals across three formats last year.