Salem reportedly sustained minor injures on his face during the fight inside the jail.
The reason behind the scuffle is unknown.
"Salem was attacked by Mustafa Dossa with sharp object. He was injured and doctors are treating him inside the jail. A police team is at the spot," Vasant Tajane, senior inspector at NM Joshi Marg police station, said.
42-year-old Salem has been convicted in the 1993 Mumbai serial blasts case and is also facing trial for the 1997 murder of music baron Gulshan Kumar. He is facing trial in connection with a total of nine cases, which includes two murders.
He has been lodged in the South Mumbai jail since his 2005 extradition from Portugal.
Mustafa Dossa, an associate of the dreaded D-company, is an accused in another 1993 serial bomb blasts case.