The sheriff's department, which patrols Compton, is searching for a second suspect, The Times reported.
The fatal shootings were at least the third and fourth in Compton since Thursday.
The shootings occurred at 1:30 p.m. Sunday in the 600 block of North Alameda Street, near Rosecrans Avenue, when a gunman drove up in a car and opened fire while the two men were passing in front of a church, said Deputy Aura Sierra of the Sheriff's Headquarters Bureau.
Both men were declared dead at the scene, Sierra said.
The vehicle was later found abandoned in the 2000 block of 127th Street, Sierra said.
According to the Los Angeles County Department of Coroner, Rigoberto Vega, 23, of Compton, was with the man in the wheelchair, whose name was withheld pending notification of relatives. According to the Los Angeles Times, that victim was identified by his sister and a neighbor as David Gallegos, 32, of Compton.
Assistant Chief Coroner Ed Winter said his office has been unable to contact the man's mother to confirm his name.
Although some media reports quoted a woman in Compton who said she was the mother, Winter said coroner's officials were told she was in Mexico, he said.
"She might be illegal and not want to talk to us," Winter said.
Gallegos was in a wheelchair because of an accidental shooting six years ago.
Rosenberg told The Times the shooting of a defenseless man in a wheelchair was an example of how brazen and vicious Los Angeles County gangs are becoming.
"As far as the rules go, whether it's shooting a guy in a wheelchair or a woman or children, those rules are changing. There's more women getting shot and more children. It used to be if a guy was with his wife and children they would wait, but not anymore," Rosenberg said.
The shooting victims were boyhood friends going to an IHOP restaurant for takeout meals, Rosenberg said.
It was unknown if the shooting was gang-related, said Derrick Thompson, also of the Sheriff's Headquarters Bureau. Neighbors and friends told Eyewitness News neither victim was a gang member.
On Thursday, Dejuan Andino, 28, of Compton, was fatally shot in the 900 block of South Essey Avenue, and around 2 a.m. Saturday, a 19-year-old man was shot to death in the 200 block of West Alondra Boulevard. It was unclear whether any of the shootings were gang-related or connected to each other, according to the Sheriff's Department.
Anyone with information regarding the shootings was asked to contact Sheriff's Homicide Detectives at (323) 890-5500.