Russell, 38, appeared to aim a blow with his right hand while on board Kings Dolly, after the horse pulled up at a pre-race 'show' hurdle.
The incident took place at the Mares' Handicap Hurdle at Tramore on Friday.
"We will examine whatever footage is available," said Denis Egan, chief executive of the Irish Turf Club.
"We will then decide then whether or not any rules have been broken."
The race-day stewards were not aware of the matter but footage appeared on social media.
Russell won the 2014 Cheltenham Gold Cup with 20-1 outsider Lord Windermere.
"I am not sure everyone on social media quite understands how a thoroughbred racehorse handles at race time but I am happy to speak with the Turf Club about this," Russell told the Irish Daily Star.
"The situation with Kings Dolly was an ordinary enough situation and I didn't do anything out of the ordinary.
"I ride every horse to win, no matter what, and would never do anything to hamper its chances."
Jockey Davy Russell is under investigation after footage appeared to show him striking a horse on the back of the head moments before a race.