Hector, 23, made the claim in a tweet after Tottenham won 2-1 to go second in the FA Women’s Championship.
“Such a shame that racism seems to be rising up again in football,” the former Watford Ladies player wrote.
“I received some monkey noises from an opposition player. The only reaction was to let football do the talking.”
Sheffield United Women said in a statement that they “are aware of the post on social media and have already begun an investigation to determine the full facts”.
Spurs, who said the alleged incident was reported to the referee by Hector during the game, also reported it to the FA.
An FA statement read: “We take all allegations of discrimination very seriously and will be making enquiries into the matter.”