Authorities have a person of interest in the investigation and are not searching for a suspect, according to Akil Davis, assistant director of the FBI's Los Angeles field office.
The person killed was near a vehicle that had been blown to pieces outside the clinic, operated by American Reproductive Centres, Davis told reporters.
The bomb, which detonated before 11am local time on Saturday (4am AEST on Sunday) was either in or near a car parked outside the clinic when it exploded, said Mayor Ron deHarte of Palm Springs, about 160 kilometres east of Los Angeles.
"Make no mistake, this is an intentional act of terrorism," Davis said, adding the FBI would determine if it was an act of "international terrorism or a domestic terrorism".
Davis did not comment on the relationship - if any - between the victim and the person of interest in the investigation.
Video posted online showed the bomb appeared to have ripped a gaping hole in one of the clinic's walls and caused damage throughout the building.
Several other buildings in the area were damaged, some extensively, authorities said.
American Reproductive Centres, 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 would be fully operational on Monday.
The clinic's laboratory, including all eggs, embryos and reproductive materials, was safe and secure, and all members of staff were unharmed, it said in a Facebook post.
"The moment has shaken us - but it has not stopped us," Maher Abdallah, who runs the clinic, said in the post.Â
With AP
