According to a report in the Daily Mail newspaper, Henry said the club wanted to limit the number of African players in their squad as "they have a bad attitude" and "cause mayhem" when they are not in the team.
A statement from the club said: "West Ham United have today terminated the contract of Director of Player Recruitment, Tony Henry, with immediate effect following his unacceptable comments that were widely reported in the press. Our action follows a full and thorough investigation.
"West Ham United will not tolerate any type of discrimination.
"The West Ham United family is an inclusive one where, regardless of gender, age, ability, race, religion or sexual orientation, everybody feels welcome and included."
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The decision follows the Football Association announcing on Thursday that it was investigating the matter, the same day that West Ham launched their own investigation and suspended Henry.
Henry joined West Ham in 2014, having previously worked for Everton, Sunderland and Chelsea.
West Ham have six first-team squad members of African descent - Cheikhou Kouyate, Pedro Obiang, Joao Mario, Angelo Ogbonna, Arthur Masuaku and Edimilson Fernandes.
Kouyate posted a message on Instagram on Thursday, saying: "African and proud".
The post was liked by team mates Obiang, Masuaku, Manuel Lanzini and Adrian.
(Reporting by Christian Radnedge; Editing by Pritha Sarkar)
