Haaland threw the ball against the back of Gabriel's head after City's John Stones scored deep in added time to salvage a 2-2 draw with 10-man Arsenal and keep his side top of the table after a rip-roaring battle against their title rivals.
An FA spokesperson said the incident involving Haaland and Gabriel was checked by the Video Assistant Referee (VAR) at the time and no further action was deemed necessary.
Arsenal had forward Leandro Trossard sent off for a second yellow card before half-time for kicking the ball away after being penalised for a challenge on Bernardo Silva.
"I just felt like I needed to put something out there which has been bothering me. Because obviously, the Trossard sending off - of course, in the moment, you're frustrated," Wright posted on Instagram.
"It's 2-1. And I'm thinking 'Yes, we've got them'. And then we get (a player) sent off for something that, let's face it, is... foolishness - what they're getting sent off for now. So, in the moment, yeah. Again, you shouldn't be sent off for that.
"But the one thing that boiled me up properly was Haaland's coward's move, bro. I saw it this morning properly. Throwing the ball in Gabi's head when he's not looking. When Gabi's back's turned to him. Real coward's move. Gabi would look him in the eye, you know.
"I'm looking at this as a really good defender vs striker for the years to come, them two. I love watching them two. And then you're doing a coward's move like that ... I thought you was bigger than that, bro. I thought you was bigger than that."
The Norwegian international Haaland, who opened the scoring against Arsenal in the ninth minute, has 10 goals in five league appearances this season in what could be a third consecutive Golden Boot campaign.
