The German defender lashed out during Saturday's 2-1 win over the Hammers at the Britannia Stadium when the two tussled at a free-kick. The off-the-ball incident left Upson requiring treatment on a cut above his eye which had been reopened.
The clash was missed by referee Martin Atkinson but after watching video evidence he informed the FA that he would have dismissed Huth had he been looking at the incident. The FA decided to charge the defender with violent conduct on Monday.
Huth and his club have accepted the player's guilt and are awaiting his punishment - likely to be a three-match ban - from the FA.
"Stoke and Robert Huth accept the FA charge of violent conduct and would like to apologise for the incident at the Britannia Stadium on Saturday,'' said a club statement.
"All players were briefed at the beginning of the season about obstructing opponents at set-plays and Robert reacted in frustration at being impeded by Matthew Upson for the second time in the game, stopping him from marking James Tomkins at set-pieces as instructed.
"Robert Huth's actions are totally out of character for a fully committed defender who has only received one red card - for two cautions - in nearly eight years of playing in the Premier League. We await the FA verdict on the incident.''
Huth's case will be discussed at a Regulatory Commission hearing on Thursday and if the versatile defender is banned, he will miss Stoke's Premier League fixtures against Tottenham Hotspur, Wolves and Hull City.