The 33-year-old former England striker, an 84th-minute substitute for Geoff Cameron, appeared to lash out at Arteta, catching him on the back with a mild punch.
But referee Chris Foy saw the incident and took no action which prevents the FA taking any retrospective action. Stoke were trailing to Lukas Podolski's deflected free-kick when the incident happened.
After the match Stoke manager Tony Pulis said: "Arteta's challenge was poor, but Michael should not do that."
Arteta revealed that the players had apologised to each other after the match.