The incident unfolded in late May after the couple, Dravon Ames and Iesha Harper, and their two young children left a Family Dollar store where the doll was allegedly stolen.
The manager called police, according to KNXV-TV, and officers pulled the couple over a short time later as they were arriving at a babysitter's home.
The parents said they did not realize their 4-year-old daughter had walked out of the store with the doll.
The officers are seen on the cellphone video, taken by a bystander, warning the couple, “You’re going to get (expletive) shot,” pointing guns at the couple and grabbing one of their children.
The officers are accused of throwing Ames, 22, against a vehicle, kicking his leg so hard he collapsed and punching him for no reason, media outlets reported.
At one point in the video, one of the officers can be heard yelling, “I’m going to (expletive) put a cap right in your (expletive) head.”
Harper, who is five months pregnant, was carrying her 1-year-old daughter when she got out of the vehicle and was handcuffed and allegedly slammed face-first into a police car after handing her daughter to a bystander.
Harper told CNN she really though the cop was going to shoot her.
No one was arrested in the incident because the store manager declined to prosecute, police said in a social media post.
The incident with the irate officers caused outrage on social media and prompted the family to file a $10 million lawsuit against the department alleging civil rights violations.
Phoenix Police Chief Jeri Williams verified the incident is under investigation, KNXV reported, and she said Friday she initiated the probe after learning of the video.
“I, like you, am disturbed by the language and the actions of our officer. I assure you that this incident is not representative of the majority of Phoenix police officers who serve this city," Williams said.
Phoenix Mayor Kate Gallego apologized Saturday, expressing concern over the incident.
"It was completely inappropriate and clearly unprofessional," Gallego said in a post on social media.
“I am deeply sorry for what this family went through and I apologize to our community,” she said.
Gallego is also holding a community meeting Tuesday to discuss the fallout and said she hopes to have officers outfitted with body cameras as soon as August, earlier than the department had planned.
Both officers involved in the incident have been removed from street patrols and reassigned to desk duty, the department said in a social media post Saturday.