Shelvey was charged by the Football Association following Swansea's 4-1 defeat to Liverpool on Monday, having caught Emre Can with his arm in an incident that went unnoticed at the time by the match officials.
The former Liverpool man took to Twitter to insist contact with Can was accidental, but Swansea issued a statement confirming they will not challenge the charge on Wednesday.
It read: "While the club supports Shelvey’s statement that the incident was unintentional, it does not believe the outcome of an appeal would prove positive for the club or player.
"Shelvey will now serve the customary three-match ban, plus an additional game for his second red card of the season.
"The ban starts immediately and the midfielder will miss tomorrow's fixture at QPR."
Swansea's game with Liverpool also featured an altercation between Raheem Sterling and Federico Fernandez.
However, the Liverpool forward has escaped punishment due to that incident being seen by the match officials, who opted to take no action.
