The harassment towards Jamaican Khadija Shaw, who is the league's top scorer, came after the team's loss to Arsenal on Sunday.
The harassment has been reported to the police by Manchester City, but when the team met Arsenal again a few days later, Shaw was not on the pitch.
We left yesterday and didn't manage to get her on the trip, said club manager Gareth Taylor after the match.
It's very hard for me to analyze. Who knows what's going on in that world? When you're affected by such things, it's very, very tough.
In a statement on Tuesday, Manchester City condemned the harassment:
"Bunny (Shaw) has decided not to share the messages publicly in order not to give oxygen to the vile individuals who sent them".