The midfielder was involved in a fight with two men, and a picture of the incident, apparently showing a shirtless Barton being held back by police and a woman, appeared on Twitter.
A Merseyside Police spokeswoman said on Monday: “Merseyside Police were called to Eberle Street in Liverpool city centre at 5.30am this morning following reports of an altercation.
“On arrival officers found a 29-year-old man who had sustained injuries to his face. The man left the scene voluntarily.
“Two 21-year-old men from the L13 area were arrested at the scene for a public order offence. They are currently in police custody.”