Carney received the abuse after Chelsea's Champions League win over Fiorentina on Wednesday with the Instagram user posting rape and death threats against the 31-year-old player.
"The FA takes such matters extremely seriously," the English game's governing body said in a statement. "The abuse of players on social networking sites is a serious concern and we call on the police and social media organisations to do everything they can to help tackle this growing problem.
"We provide all our senior England players with training, guidance and support on the use of social media and treat our duty of care in this regard with the utmost importance."
Carney, who has 133 international caps, did not report the incident to the police, according to the BBC.
Responding to the post, she said: "Wow, some people..."
The England Women's coach, former Manchester United defender Phil Neville, highlighted the abusive message on his Instagram account, describing it as "absolutely disgraceful."
A spokesperson for Instagram told British media: "We do not tolerate threatening or abusive behaviour, and the account that sent these messages has been removed from Instagram."
Chelsea captain Carney scored the only goal in their round of 16 home first-leg clash against the Italian side.