Benjamin Mendy, 27, is due to appear in court on Friday and has been suspended by City pending an investigation.
The force said the charges relate to three complainants, over the age of 16, and are alleged to have happened between October last year and this month.
France international Mendy has been remanded in custody ahead of his appearance at Chester Magistrates’ Court, police said.
A police spokesman said: “Cheshire Constabulary and the Crown Prosecution Service would like to remind everyone that criminal proceedings against Mendy are live and that he has a right to a fair trial.”
Mendy joined City from Monaco in 2017 and has since been part of three Premier League title-winning squads, as well as lifting the English League Cup twice.
In a statement, Manchester City said: “Manchester City can confirm that following his being charged by police today, Benjamin Mendy has been suspended pending an investigation.
“The matter is subject to a legal process and the club is therefore unable to make further comment until that process is complete.”
Since his arrival at City four years ago, injuries have limited his playing time, with the defender undergoing knee surgery in the 2018-19 season.
Mendy, who has played for France 10 times and won the World Cup in 2018, played against Tottenham on the opening weekend of the Premier League season but didn’t feature against Norwich last weekend.
City host Arsenal in the Premier League on Saturday.