ABC News, citing law enforcement sources and the facility, said at least five people were injured in the explosion.
The Palm Springs City government said in a Facebook post an explosion occurred before 11am local time on Saturday (4am AEST on Sunday).
"It has been identified as a bomb that was either in or near the car," Mayor Ron DeHarte told Reuters on Saturday.
The Federal Bureau of Investigation in Los Angeles said in a social media post it was investigating the explosion with bomb technicians deployed to the scene.
California governor Gavin Newsom has been briefed on the explosion, his office said.
Dr Maher Abdallah, who runs the American Reproductive Centre fertility clinic, confirmed his clinic was damaged but said all his staff were safe and accounted for.
The explosion damaged the practice's office space, where it conducts consultations with patients, but left the IVF lab and all of the stored embryos there unharmed.
"I really have no clue what happened," Abdallah said. "Thank God today happened to be a day that we have no patients."
Aerial footage showed a burned-out car in a parking lot behind the building that housed the fertility clinic's office space.
The blast caved in the building's roof and blew a wide debris field across a sidewalk and four lanes of the street on the other side of the structure.
Rhino Williams, 47, was inside the Skylark Hotel just over a block away from the scene when he heard a huge boom. He said he saw a building had "blown out" into the street, with bricks and debris scattered everywhere, and spotted a car's front axle on fire in the building's parking lot.
Nima Tabrizi, 37, of Santa Monica, said he was inside a cannabis dispensary nearby when he felt a massive explosion.
"The building just shook, and we go outside and there's massive cloud of smoke," Tabrizi said.
"Crazy explosion. It felt like a bomb went off. ... We went up to the scene, and we saw human remains."
Palm Springs is a tiny community in the desert about a two-hour drive west of Los Angeles, known for upscale resorts and a history of celebrity residents.
With AP
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