The unnamed male is believed to have used photographs of the Italian forward taken in a nightclub as a way of making financial gain.
"Police are investigating after an allegation of blackmail was made by a Premier League football club," said a Greater Manchester Police spokesman.
"A man has been arrested and bailed. Inquiries are ongoing."
The incident is said to have taken place just hours of Balotelli had featured in City's 1-0 loss to Swansea City.