Bellamy was punished retrospectively for striking Swansea midfielder Jonathan de Guzman off the ball, an incident that went unseen by match official Andre Marriner during Saturday's Premier League game at the Liberty Stadium, which the home side won 3-0.
The former Wales international had until 6pm on Tuesday to appeal the charge, but decided against contesting the decision and he will serve a three-match ban.
A statement posted on the club's official Twitter account said: "Craig Bellamy has reluctantly accepted the FA charge in relation to an incident at the Liberty Stadium on Saturday 8 February.
"Both Craig and the club are disappointed that the three-man panel of former referees reached their decision based on a video review this week.
"Following internal discussions at the club, Craig has chosen to accept the charge and the three-match ban without appeal."
The suspension began immediately on Tuesday, with Bellamy ruled out of the home fixture with Aston Villa, as well as Saturday's FA Cup fifth-round tie with Wigan Athletic and the game with Hull City on February 22.
