The victim was identified as Anthony Rivera, 48, of Los Angeles.
The hijacking occurred about 12:45 a.m. Wednesday near Manchester Avenue and Figueroa Street, according to the LAPD.
The bus was pursued by authorities from South L.A. to downtown, where SWAT officers arrested the suspect. Paramedics took the wounded man from the bus to a hospital, where he died.
Another passenger and the bus driver were rescued.
Police arrested 51-year-old Lamont Campbell of Los Angeles, who remains in custody. A case against him will be presented to the district attorney's office on Monday, the LAPD said.
Wednesday's shooting and hijacking is the latest in a series of violent attacks on the transit system and has renewed safety concerns on Metro buses and subways.
Metro says it's working on a new weapons-detection system and other safety measures.
City News Service contributed to this report.