The 28-year-old joined the German side last month but the club have taken action following his post on Instagram.
Mainz announced on Tuesday that they have suspended him for the now-deleted post, deeming it 'unacceptable'.
A club statement read: "FSV Mainz 05 have relieved Anwar El Ghazi of his training and matchday-related duties.
"The decision comes as a result of a since-deleted social media post from the 28-year-old that appeared on Sunday evening.
"In the post, El Ghazi took a position on the ongoing conflict in the Middle East that was deemed unacceptable by the club.
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"Prior to making this decision, the club and the player had engaged in an in-depth discussion.
"Mainz 05 respect the fact that there are varying perspectives on the decades-long, complex conflict in the Middle East.
"However, the club are distancing themselves from the content of the social media post in question, as it does not align with the values of the club."
El Ghazi has made just three appearances for Mainz since he completed his move to the Bundesliga.
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He spent most of his Premier League career at Villa, for whom he scored 26 goals in 119 appearances across all competitions.
The Dutchman also played on loan at Everton for the second half of the 2021/22 season, featuring twice for the Toffees.
Manchester United were reported to be considering a shock move for El Ghazi in the summer before he moved to Mainz.