Following his 6-3 7-6(4) defeat Young took to Twitter to offer his views on what had happened.
"I'm shocked and disappointed, Ryan Harrison, to hear you tell me how you really feel about me as a black tennis player in the middle of our NY match.
"I thought this was supposed to be an inclusive gentleman's sport," the 28-year-old world number 65 said.
Young did not elaborate on what was actually said between the pair, but Harrison was quick to respond.
"The accusations made by Donald Young tonight following our match are absolutely untrue," he said on Twitter.
"I'm extremely disappointed that someone would say this in reaction to a lost tennis match. Any video/audio will 100 percent clear me and I encourage anyone with the available resources to find it."
The ATP issued a statement later saying it had begun an investigation into the matter.
"The ATP takes any allegations of racial prejudice extremely seriously. A further review of all video and audio recording from the match will take place as this matter is investigated further," it said.
"No further comment will be made until the completion of the investigation."
United States Tennis Association spokesman Chris Widmaier said the organisation would stay in close contact with the ATP during the investigation.
Straight after the match Harrison gave an interview in which he said any bad feeling had been in the heat of the moment.
"At the end of the day, you see everybody, you like everybody and you want to be friends and friendly with everybody, but everybody out here I compete against, even the ones I like, they are the ones trying to take away my livelihood," he said.
"I have to do what I can to get through, and I was proud of myself for doing that."
(Reporting by Martyn Herman; Additional reporting by Frank Pingue in Toronto; Editing by Toby Davis)
