Marcus Herrera, 23, was arrested Sunday on suspicion of killing 55-year-old Robert Musial, who was found by police officers around 7:20 p.m. Friday.
The officers were responding to a request for a well-being check on a man who had been asking for help near Sharon Art Studio in the park, police spokesman Sgt. Mike Andraychak said.
Musial appeared to be experiencing a medical emergency, and lost consciousness before an ambulance arrived. Emergency crews tried to revive him but he was pronounced dead at the scene, Andraychak said.
A preliminary autopsy by the medical examiner's office indicated that Musial had suffered blunt-force injuries, and the case was ruled a homicide, according to Andraychak.
Herrera was identified as a suspect in the case and was brought to the San Francisco Hall of Justice for questioning. He was subsequently arrested on suspicion of homicide, robbery and assault with a deadly weapon, Andraychak said.
Investigators believe other people in the park witnessed the crime, and are asking anyone with information about it to call police Sgt. John Burke at (415) 553-1145.
People wishing to remain anonymous are encouraged to call the Police Department's anonymous tip line at (415) 575-4444 or send a tip by text message to TIP411.