The Argentine tumbled to the ground as he was tested by safeguard Erik Pieters and the Hammers were granted a punishment, which put them 1-0 up in a 3-0 triumph.
Lanzini is relied upon to challenge the charge."The official was 10 yards from the ball with nothing obstructing his vision," said West Ham chief David Moyes.
"It is clear to see the safeguard makes an endeavor to go for the ball and doesn't get it.
"From my perspective, they are conflicting with the official, whoever the board were."
Lanzini has until 18:00 GMT on Tuesday, 19 December to react to the charge.
The occurrence was alluded to a free three-man FA board who regarded he had betrayed the official.
On the off chance that the charge is maintained, he is set to get a two-coordinate boycott that would preclude him of Tuesday's League Cup quarter-last against Arsenal and Premier League amusement at home against Newcastle on Saturday.
The FA board incorporates one previous match official, one ex-director and one ex-player, and each of the three needed to concur for a boycott to be implemented.
Everton forward Oumar Niasse was the main Premier League player to be prohibited for plunging after new FA laws to rebuff reenactment were presented in May.
He was restricted for two diversions subsequent to winning a dubious punishment, under strain from Scott Dann, in a draw at Crystal Palace on 18 November.
Graham Scott was the official for West Ham's prevail upon Stoke, who were left in seventeenth place - one point over the transfer zone - after a third group overcome consecutively.
"He's plainly plunged. He's a shrewd player, he'll draw a foul or some sort of test however he wasn't cut," said Stoke manager Mark Hughes after the match.
"Officials need to get coordinate characterizing choices right and he positively didn't get that one right."
