"Inzamam is unlikely to be available for the first Test, he has conveyed this to the team management," Pakistan manager Haroon Rasheed said.
Pakistan vice-captain Yousuf Youhana is also doubtful for the first Test, which begins on Friday, and Rasheed said he would undergo an examination on Tuesday.
"Youhana also has a hamstring problem like Inzamam and he is feeling uncomfortable batting and fielding," he said. "He will be examined by doctors, only then will we know if he can play in the first Test. His chances at the moment are 50-50."
Inzamam, a veteran of 88 Tests and 298 one-day games, also missed two matches of the one-day series against South Africa with a strained hamstring, and was virtually a passenger on Sunday after straining the muscle again while batting.
In his absence Youhana led the side in the third and fourth games of the five-match
Former captain Rashid Latif is also not available after pulling out of the Test series for personal reasons.
Wicketkeeper Latif stepped down as captain just before the series against South Africa after completing a five-match ban for taking a disputed catch during the third Test against Bangladesh last month.
But Latif said that if there was a genuine captaincy crisis he would reconsider his decision not to play in the Tests.
"I have made my decision but if the circumstances dictate otherwise and if the board and selectors want me, I can rethink," he said.
Pakistan Cricket Board (PCB) media manager Samiul Hasan said that the squad for the first Test would be announced on Tuesday.
Inzamam, Rashid and Youhana are the three most senior players in the team followed by Abdul Razzaq, Shoaib Akhtar and Younis Khan. PCB sources ruled out a recall for former captain Moin Khan, who was dropped after the 2001 New Zealand tour.