The Cardinals said they became aware of the situation Wednesday and are co-operating with the investigation.
"Given the serious nature of these allegations we have taken the immediate step to deactivate Jonathan from all team activities," the team said in a statement.
The NFL said the case will be reviewed under the league's personal-conduct policy.
One of the counts was "aggravated assault causing a fracture" involving the 27-year-old victim, whom they did not identify. Police said they were carrying out a search warrant of Dwyer's residence in pursuit of more evidence.
Police said that in interviews with detectives, the 25-year-old player denied committing any assault.
There was no reply to telephone message left for Dwyer's agent, Adisa Bakari, seeking comment Wednesday.
Authorities depicted a stormy relationship between Dwyer and the woman that escalated into violence on July 21, four days before the Cardinals reported to training camp.
Neighbours heard a fight and called police, who showed up at the residence but left without making an arrest because Dwyer hid in the bathroom and the woman said no one else was at the home, Sgt. Trent Crump said.
"She said she was in an argument on the phone only," Crump said.
The next day, Crump said, Dwyer snatched the woman's cellphone and threw it from the second floor of their residence to prevent her from calling police about another dispute.
Crump confirmed there was an allegation that Dwyer threw a shoe at or toward his son. Crump said he couldn't elaborate on it.
Crump said the woman moved out of state with the child, but came forward last week and provided police with information about her injuries and text messages indicating Dwyer "was going to harm himself because of what had been going on."
The NFL has been rocked by domestic violence issues ever since a videotape surfaced that showed former Baltimore Ravens running back Ray Rice knocking out his then-fiancee in an Atlantic City, New Jersey, elevator. Then Minnesota Vikings star running back Adrian Peterson was indicted on felony child-abuse charges. On Wednesday, the Carolina Panthers decided that star defensive end Greg Hardy will not play any more games for the team until his domestic violence case is resolved.
Hardy was convicted of assault on a female and communicating threats after the victim said the 6-foot-4, 275-pound player threw her in the bathtub and onto a sofa covered with guns before threatening to kill her. Hardy is appealing the ruling.
Critics have been calling for NFL Commissioner Roger Goodell's resignation for his handling of Rice's case. Rice was originally suspended for two games, then banned indefinitely after the video surfaced of his attack in the casino elevator.
This is the second domestic violence case involving a Cardinals player. Inside linebacker Daryl Washington pleaded guilty to assaulting his ex-girlfriend and is serving a year of supervised probation. Washington has not yet been penalized by the NFL for the offence but is suspended for this season for violating the league's substance abuse policy.
Dwyer was led into the jail in handcuffs to be booked on counts that include aggravated assault causing a fracture and involving a minor, criminal damage and preventing the use of a phone in an emergency.
The Maricopa County Sheriff's Office, which runs the jail, said Dwyer has refused all media interviews.
Dwyer signed with the Cardinals this year and was their second-string running back after spending the last four seasons with the Pittsburgh Steelers. He scored a touchdown last week in Arizona's victory over the New York Giants.
His best year for Pittsburgh was 2012 when injuries depleted the team's backfield in the middle of the season and Dwyer filled in and had 100-yard-plus games in consecutive weeks.
Dwyer, from Marietta, Georgia, was a sixth-round draft pick of the Steelers out of Georgia Tech in 2010.
AP Sports Writer Bob Baum in Phoenix contributed to this report.