Everton fell to a dissapointing 1-0 home defeat to Fulham on the opening day of the Premier League season. Striker Maupay missed a number of chances and after the match was abused on social media.
"This is what I get for not scoring. No one should ever deal with this," Maupay wrote on his Instagram story alongside a screenshot of the abuse he received.
In an official statement, Everton said: "We stand firmly against such behaviour and are investigating the accounts that have targeted Neal. Everton Football Club condemns all forms of personal abuse directed towards our players and their families or any club staff on social media.
"We encourage anyone using these platforms to report, condemn and highlight any such abuse to the social media platforms on which it appears. Discrimination and hate has no place in our game."
Fulham sent their own message of support to the attacker, saying: "We stand with Neal Maupay and support Everton's message to report, condemn and highlight such abuse."
The striker's Everton team-mate Idrissa Gueye posted a message in defence of Maupay, saying: "We win together and lose together. We all know the hard worker that you are."
After the match, Everton boss Sean Dyche told BBC Sport: "I want all players to get in the right areas and Neal did. You have to keep getting there to score goals. Eventually, if you create that many chances and keep doing it relentlessly, you will score goals and win games. That is what I have learned in my life in football."
Everton's next match is a trip to Aston Villa, who started the season with a 5-1 defeat at the hands of Newcastle.