Farrell was struck on the right side of his jaw Saturday by a ball off the bat of Jalen Miller with one out in the ninth inning.
The Rangers say Farrell had 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 is the son of former Red Sox manager John Farrell. He became the first son to pitch against a team managed by his father in 2017 while with Cincinnati.
The Giants and Rangers finished in a scoreless, nine-inning tie.