Joeboury Coleman, 27, of Los Angeles, was arrested Sunday and is being held without bail, according to the LAPD.
Video posted on social media shows a man grab a dog by the collar and then drop it down the stairwell.
Officers responded to the 4000 block of Oakwood Avenue around 3:30 p.m. after reports of a man abusing a dog.
"Concerned citizens had provided information about videos posted on social media showing a dog being abused at the location, including being kicked and thrown from a multi-story stairway by a male individual," the LAPD said in a news release.
A man who appeared in the videos was detained in an alley behind the building, police said.
"[Officers] conducted a follow-up to the individual's apartment and located the dog shown in the social media video, kicked and thrown from the stairway," police said.
The 7-month-old female dog was taken to an animal shelter and is receiving treatment for a broken hind leg, which may need surgery. Police said the dog was also malnourished.
Anyone with information on the alleged abuse is asked to contact detectives at (213) 484-3490.