The Cardinals deactivated Dwyer after news of the arrest, according to a news release from the team.
CNN's calls to the office of Dwyer's agent, Adisa Bakari, weren't immediately returned.
An announcement from the Phoenix Police Department said two incidents allegedly occurred on consecutive days in late July. They were reported last week.
Detectives interviewed Dwyer, and he "admitted to the incidents, however, denied any physical assaults," the police statement said.
According to a court document, the incident began the morning of July 21, when after a verbal argument with his wife at their Phoenix apartment, Dwyer allegedly tried to kiss his wife and remove her clothing.
She told him to stop several times, and "when he continued, she bit the defendant's lip. He head-butted her in the face, which she later learned had caused a nasal bone fracture."
A neighbor called police because of "the loud arguing," and when they arrived, Dwyer's wife told them that only she and her son were in the house, the document says. Dwyer acknowledged Wednesday that he was hiding in a bathroom at the time, according to police.
Dwyer's wife said that the running back texted a photo of a knife, saying he didn't want to live, and threatened to kill himself in front of her and her son if she told police about the assault, the document says.
On July 22, there was another argument, and Dwyer allegedly punched his wife on the left side of her face, according to the court document.
"He also began punching the walls, causing visible damage. The defendant then picked up a shoe and threw it, striking their 17-month-old son in the stomach," it says. The child was not injured.
When his wife threatened to call police, Dwyer allegedly took her phone and threw it from their second-story residence, the document says. As his wife fled, witnesses heard her yell, "He f---ing hit me; I'm calling the police." Witnesses also reported seeing "swelling and discoloration" on the left side of her face, according to police.
Police said he was booked on one count of aggravated assault causing a fracture, one count of aggravated assault involving a minor, two counts of criminal damage, one count of preventing the use of a phone in an emergency, and assault.
The two victims were a 27-year-old woman and an 17-month-old child, police said.
Dwyer posted bond and was released from the Maricopa County Jail on Thursday, according to a tweet from the county Sheriff's Office.
The state had requested a $60,000 bond Wednesday, but the judge set a $25,000 "cash-only" bond and required Dwyer to wear an electronic monitoring device and abide by a curfew. He also can't have contact with the victims, leave the state of Arizona, possess weapons or drink alcohol.
The Cardinals said they became aware of the allegations when contacted by police.
Dwyer, 25, is the fourth NFL player to be in the headlines this week. Two other players, Adrian Peterson of the Minnesota Vikings
and Greg Hardy of the Carolina Panthers
, took paid leave from their teams to focus on their legal cases.
Peterson has been charged in Texas with child abuse. Hardy has been convicted of misdemeanor assault charges in North Carolina and has been granted the opportunity to have a new trial, this time in front of a jury.
And running back Ray Rice has an appeal with the NFL in connection with his indefinite suspension after a domestic violence
Dwyer is listed as the No. 2 running back for the Cardinals behind Andre Ellington. He is in his fifth NFL season and first with the Cardinals, and he has 51 yards on 16 carries in two games this year.