The bomb was either in or near a car parked outside the clinic when it exploded, Palm Springs mayor Ron deHarte said.
Palm Springs police chief Andy Mills said in a statement the blast "appears to be an intentional act of violence" and that several buildings were damaged, some severely.
"There has been one fatality, the person's identity is not known," Mills said.
Maher Abdallah, who runs the American Reproductive Centres 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."
The FBI in Los Angeles said in a social media post that it was investigating the explosion, with bomb technicians deployed to the scene.
ABC News, citing law enforcement sources and the facility, which was operated by American Reproductive Centres, said at least five people were injured in the explosion.
Palm Springs is about 161 kilometres east of Los Angeles.
The Palm Springs city government said in a Facebook post an explosion occurred before 11am local time on Saturday (4am AEST Sunday).
Photos posted online showed the single-story structure that houses the clinic after the explosion.
The bomb appeared to have ripped a gaping hole in one of its walls, leaving a pile of mangled debris spilling into the street. Tiles on its roof were dislodged or missing.
California governor Gavin Newsom has been briefed on the explosion, his office said.
American Reproductive Centres are (ARC), which has offices in at least three California cities, provides services including in vitro fertilisation, genetic testing and in-house egg donation.
Despite damage to the building, ARC said the facility will be fully operational on Monday.
With AP
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