The Karachi-based player suffered the injury while playing in a Patrons Trophy match and that rules him out of the warm-up match against the West Indies at Bagh-e-Jinnah.
Young fast bowler Irshad Ali in the local side has replaced Sami.
Samis poor form saw him being dropped before the Champions Trophy and also overlooked for the first two Test matches against the West Indies. But with pace spearheads Shoaib Akhtar and Mohammad Asif banned for failing dope tests, the pacers prospect of a comeback looked quite bright.
A Pakistan Cricket Board official, however, expressed hopes that Sami would be okay before the final Test and is likely to be considered for the Karachi match.