The 30-year-old Frenchman was admitted to hospital for treatment on his eye, nose, and lip.
Barton could face a court case for assault as Dabo has asked police to press charges.
A police spokeswoman said: "Greater Manchester police has received a report from a 30-year-old man that he was assaulted. Inquiries are ongoing."
Barton, 24, has been suspended for the rest of the season by City and could be sold in the summer after a history of bad behaviour.
Dabo revealed on Thursday he is in talks with his lawyers over suing Barton for the training ground bust-up.
In December 2004, Barton was fined six weeks' wages after he stubbed a cigar into team-mate Jamie Tandy's eye at the club's Christmas party.
Seven months later, Barton was fined eight weeks wages after a scrap with team-mate Richard Dunne and a 15-year-old Everton fan.
In March, Barton was arrested on suspicion of assault and criminal damage in an argument with a taxi driver in Liverpool.
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