Harrison beat Young in the New York Open on Monday, but the match was marred by an on-court argument between the two in the first set, which left them needing to be separated by officials.
Young subsequently accused American compatriot Harrison of racism, posting on Twitter: "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."
Harrison responded in a tweet that read: "The accusations made by Donald Young tonight following our match are absolutely untrue. I'm extremely disappointed that someone would say this in reaction to a lost tennis match.
"Any video/audio will 100 per cent clear me and I encourage anyone with the available resources to find it."
Addressing the issue, an ATP spokesperson said: "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.
"No further comment will be made until the completion of the investigation."