Abe allegedly grabbed his 18-year-old daughter and forced her to the floor at their home in central Tokyo on Monday evening, reported national broadcaster NHK and Kyodo News, citing unnamed police sources.
The 47-year-old former star catcher, who is among baseball-obsessed Japan's most recognised sports figures, was released early Tuesday, the reports said.
Tokyo Metropolitan Police declined to comment when contacted by AFP. The team did not immediately respond to a request for comment.
Abe reportedly told investigators that he was trying to mediate a fight between his daughters, aged 18 and 15, Kyodo said.
He allegedly had been drinking and became furious after his older daughter talked back to him, then was arrested at home in front of his daughters and wife, Kyodo said.
His 18-year-old daughter reported the incident to child protective services, the Mainichi Shimbun said.
The Giants are Japan's oldest and arguably most popular baseball team, often compared to the New York Yankees.
Giants president Toru Kunimatsu issued a statement saying violence cannot be tolerated, local media reported, and that the team will be considering what steps to take next.
