The footage of the attack, believed to have taken place in the Northfield area of Birmingham, has been viewed millions of times online.
West Midlands Police have now urged anyone who has shared the footage to delete it from their accounts because it may impact on legal proceedings.
The teenager remains in police custody.
Officers have already spoken to two other individuals, a police spokesman said, and "plans are in place" to arrest a second girl.
Insp John Askew said: "The response from members of the public, clearly disgusted by what they've seen online, has been overwhelming and we've had lots of people getting in touch to provide names of those [suspected of being] responsible.
"I would like to reassure everyone this is being treated very seriously and that the enquiry is progressing quickly."
A 16-year-old girl has been arrested on suspicion of robbery in connection with an attack on two girls which was filmed and posted online.