Police say a man, 28, was arrested after a "significant struggle with officers" in the early hours of Friday.
A police officer involved in the arrest suffered a broken wrist.
In a statement, the rugby league club said it was investigating an "incident" early on Friday morning involving Mr Moore.
Greater Manchester Police said a Taser was "deployed" during the incident, which began when a Mercedes car was spotted by officers shortly after 03:55 BST driving at speed on the East Lancashire Road, Wigan.
Police followed the car to Arrow Street, Leigh before they arrested the man on suspicion of theft and assault.
A spokesman for the Wildcats, who finished eighth in Super League last season, added: "Having spoken to Scott briefly over the weekend, the club have opened an investigation into the matter, and await further reports from the police.
"There will be no further comment at this time."
The arrested man has been bailed until 3 December.
Wakefield Trinity Wildcats are investigating player Scott Moore after a man was arrested for assaulting a police officer.