N'Zogbia, who scored a last-minute winner for Wigan in their 3-2 victory over Arsenal in the Premier League on Sunday, was held by officers on Wednesday at a test centre in Greater Manchester.
Wigan manager Roberto Martinez said the player had been "badly advised."
Newspapers said staff from the centre had become suspicious about a man who turned up to take the theory part of the driving test some weeks ago.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
They reported that 23-year-old N'Zogbia was arrested as he was about to get into a car with an examiner for the practical test.
"At about 8.30 a.m. on Wednesday, police working alongside the Driving Standards Agency arrested a 23-year-old man at Sale driving test centre on suspicion of fraud by false representation," Greater Manchester Police said in a statement.
The player has been released on police bail until June 3.
"The way I see the whole situation is that Charles has been badly advised, and he's made a naive mistake," Martinez told a reporters.
"We're going to look into every single detail before I give my full side of the story but what is important is Charles has reacted in a very mature way.
"We'll collaborate with the police and with Charles to make sure we get out of this situation in a positive way."
The offence of fraud by false representation carries a maximum jail term of 10 years.
(Reporting by Michael Holden; Editing by Steve Addison/Kevin Fylan)
