The suspect, Gregory Vanhuisen, 32, of Byron had been jailed at the county facility since March 23, after being booked by Oakland police on suspicion of robbery, Alameda County Sheriff's Sgt. J.D. Nelson said.
Nelson said he is not releasing the name of the victim or why he was there, pending notification of the man's relatives.
The two "had been cellmates for a little while" when a fight broke out in the cell Friday night, Nelson said.
Deputies, alerted to the fight at 8:13 p.m., found the man with head wound injuries. He was not breathing, Nelson said. After failing to revive him, jail medical staff members pronounced him dead about 8:42 p.m.
The last time an inmate died after a fight broke out at the jail was in August 2007, when Abdule Graham, 31, of San Leandro was killed after a fight with an inmate in a public shower.
Investigators later said Graham's injuries were caused by an undiagnosed medical condition.
The Santa Rita Jail houses nearly 4,000 inmates.