The Jamaican football player received the messages after Sunday's 3-4 defeat at home against Arsenal.
The club does not go into details about what was written and states that Shaw chose not to make the messages public because she does not want to give publicity to the "vile individuals" who wrote them.
Manchester City says that the relevant authorities have been contacted and that an investigation will be conducted.
The 28-year-old Shaw tops the top scorer list in the Super League with nine goals and has made a total of 86 goals during her years in the club, according to the BBC.
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