Farrell was hit by a shot from Giants prospect Jalen Miller in the ninth inning in Scottsdale, Arizona.
The right-hander fell to the ground but walked off the field under his own power, holding a towel to his jaw.
The Rangers say Farrell underwent a CT scan and X-rays, which revealed a non-displaced fracture in the jaw. He was released from the hospital a few hours later and is expected to visit a maxillofacial specialist Monday.
Farrell, 27, is entering his third MLB season. A reliever, he was 3-4 with a 5.17 ERA in 20 games for the Chicago Cubs last season.
The Los Angeles Angels acquired Farrell off a waiver claim in September, but he never pitched for them and was designated for assignment. The Rangers acquired Farrell, who is the the son of former big league manager John Farrell, off waivers in January.
The Associated Press contributed to this report.