Roddick, 31, did not say what year the incident happened but the two had a very public row during the 2008 US Open in New York.
"I won't say his name, I'll just say it rhymes with 'Schmovak Schmokovic'," Roddick said on a panel discussion on the American sports network Fox.
"We got into it at the US Open one time," Roddick continued. "I was kind of talking trash and he came out and beat the pants off of me as he would.
"But then he kind of chirped afterward and he came straight in, I went right up to him and had him up against the locker, but then I realized his trainer was about a little bit bigger."
Roddick, who retired in September after the US Open, said he stopped when he realized the confrontation might escalate.
"I kind of checked myself. My trainer is about five-foot-eight, 130 ... I kind of backed off real quick. I was about to get railroaded from the side."
Roddick is a former world number one ranked tennis player whose only major championship came at the 2003 US Open.
Serbia's Djokovic, who is one of the most well-liked players on the ATP Tour, has seven grand slam titles, including four Australian Open crowns.