Pakistan also released Naseem Shah and Sarfaraz Ahmed apart from Shaheen and Babar.
"Wishing Team Pakistan the best of luck! Rooting for a strong comeback. We're all cheering for you!" Shaheen wrote on X.
The changes to Pakistan's squad were made by a newly-formed selection committee, formed hours after the hosts' suffered an embarrassing loss by an innings and 47 runs to England in the first Test at Multan. Pakistan are 0-1 behind in the three-match Test series against England and are also at the bottom of the ongoing World Test Championship standings.
A statement from Pakistan Cricket Board (PCB) said taking into consideration the current form and fitness of key players and looking ahead to Pakistan's future assignments in the 2024-25 international cricket season, the selectors have decided to give rest to Babar, Shaheen, Naseem and Sarfaraz.
Babar had not scored a Test half-century since 2022 and has seen a dip in form in a year where he was made captain and then quit the post after Pakistan suffered a group-stage exit in this year's T20 World Cup in June. Shaheen, meanwhile, has struggled to find his wicket-taking groove in Tests since returning from a knee injury.
The second Test between Pakistan and England will be played on the same pitch as the series opener in Multan from Tuesday.
Pakistan squad for second and third Tests: Shan Masood (captain), Saud Shakeel (vice-captain), Aamir Jamal, Abdullah Shafique, Haseebullah (wicket-keeper), Kamran Ghulam, Mehran Mumtaz, Mir Hamza, Mohammad Ali, Mohammad Huraira, Mohammad Rizwan (wicket-keeper), Noman Ali, Saim Ayub, Sajid Khan, Salman Ali Agha and Zahid Mehmood.