Zverev told the umpire: "He just said the most famous Hitler phrase there is in this world. This is unbelievable."
A man wearing a blue baseball cap was singled out as the alleged culprit and then ordered to leave the arena.
Speaking after the match, he said: “He started singing the anthem of Hitler that was back in the day - Deutschland Uber Alles - it was a bit too much.
"He was getting involved in the match for a long time and I don't mind it. I love when fans are loud, I love when fans are emotional, but I think me being German, and not really proud of that history, it's not really a great thing to do.
"And him sitting in one of the front rows, a lot of people heard it. If I just don't react, I think it's bad from my side."
However, Zverev stressed that he did not let the incident rattle him, and he duly went on to complete a memorable victory.
He said: “Look for me it's not a very smart guy, the guy who did it. At the end of the day, I said what I said, the umpire said 'Okay we're going to get him out' and that's what he did.
"It's his loss because he didn't get to watch the final two sets."
US Tennis Association spokesman Chris Widmaier said: "A disparaging remark was directed toward Alexander Zverev. The fan was identified and escorted from the stadium."
Alexander Zverev complained to an umpire (Photo: Getty)
When Adolf Hitler rose to power in the 1930s, the Nazi Germany regime rewrote the first verse of the Deutschlandlied anthem to emphasise what they saw as Germany's superiority to all other nations. They included the lyrics "Deutschland über alles, über alles in der Welt," which means "Germany over everything, over everything in the world."
However, the Allies prohibited the public singing of the anthem after the war and neither West Germany or East Germany kept the controversial first stanza of the hymn. The current national anthem of Germany omits both the first and second verses, starting with the third verse: "Einigkeit und Recht und FreiheitFür das deutsche Vaterland," which is translated as "Unity and justice and freedom, for the German fatherland."
Former Australian professional Rennae Stubbs said shortly after the Zverev incident on Monday that there were fans during US Open night matches that were "not good."
Writing on Twitter, she said: “I love the fans but at this point there are some bad characters.
"I had a drink thrown on me last night by a drunk fan who was fighting with her boyfriend. Now we got someone yelling Hitler slurs! Wtf? Come on peeps."
