Owen appeared to thump Arsenal midfielder Arteta on the back towards the end of the 1-0 defeat at the Emirates.
The striker was not booked but the FA could investigate after it was caught on camera.
Stoke boss Tony Pulis said: "Arteta's challenge was poor, but Michael should not do that."
The Potters had fallen behind to Lukas Podolski's deflected free-kick when Arteta challenged Stoke substitute Owen.
Former England international Owen reacted angrily and appeared to lash out at the Spaniard, but referee Chris Foy did not book the 33-year-old.
"If Michael has done what he has done and they look at it, then they will deal with it," added Pulis.
"We'll see what they say. Obviously I am going to be biased as it is my football team."