Omenihu was booked at the Santa Clara County jail and was released after he posted bail. Omenihu was also served with a restraining order.
Police arrived at a residence at 4:39 p.m. local time after a woman called to report that Omenihu, who is her boyfriend, pushed her to the ground during an argument. No visible injuries were observed on the woman, who did complain of pain in her arm but declined medical attention, police said.
The case will be submitted to the Santa Clara County District Attorney's Office for possible charges.
"We are aware of the matter involving Charles Omenihu and are in the process of gathering further information," the 49ers said in a statement.
The NFL said Wednesday that, "the matter will be reviewed under the league's personal conduct policy. There is no change to his status."
Omenihu, 25, is a key member of the team's defensive line rotation and has 4.5 sacks this season. He also had two sacks and a forced fumble in the 49ers' 41-23 wild-card victory over the Seattle Seahawks. He played 15 snaps in the 49ers' 19-12 divisional round victory over the Dallas Cowboys and injured his oblique but was able to return to the game.
The 49ers will visit the Philadelphia Eagles on Sunday in the NFC Championship Game.