The former England striker will face no punishment as referee Chris Foy deemed the incident unworthy at the time, preventing the governing body from retrospective action.
Stoke City striker Michael Owen will face no action from the Football Association after appearing to lash out at Arsenal midfielder Mikel Arteta during the Gunners' 1-0 win on Saturday.
The 33-year-old striker, an 84th-minute substitute for Geoff Cameron, looked to catch Arteta on the back with a punch late in the game following a strong challenge from the Spaniard.
However, as referee Chris Foy deemed the incident unworthy of punishment at the time, the FA is prevented from taking any retrospective action.
After the match, Stoke boss Tony Pulis told reporters: "Arteta's challenge was poor, but Michael should not do that."
Speaking to reporters himself, Arteta explained that the two players had apologized to one another after the final whistle and both were keen to move on from the incident.