0419 GMT February 28, 2020
The Spanish top seed, who has never won the season-ending event, came into the tournament at London's O2 Arena under an injury cloud and was well short of his imperious best as he went down 6-2, 6-4, AFP reported.
In the earlier round-robin match in Group Andre Agassi, sixth seed Tsitsipas beat Daniil Medvedev 7-6 (7/5), 6-4, admitting their spiky relationship had made his job tougher.
Nadal is locked in a battle with Novak Djokovic to finish as the year-end number one but was not serving flat out in practice last week due to an abdominal strain that forced him to pull out of the Paris Masters at the semifinal stage.
Nadal dug deep, urging himself on but his 22-year-old opponent proved too strong. He did not concede a single break point in the entire match.
Zverev hit a total of 26 winners – double his opponent's tally – and Nadal managed just three forehand winners in the entire match.
"The physical issue was not an excuse at all," said the Spanish 19-time Grand Slam champion, who said he did not feel any pain from his abdominal injury. "The only excuse is I was not good enough tonight."
"We knew that it was going to be tough, because the period of time since the injury until today is very short, but we are here trying," he added.
Nadal faces a tough task now to qualify for the semifinals from the group phase, with matches still to come against Tsitsipas and Medvedev.
Earlier, Tsitsipas made light of a 5-0 losing record against his Russian opponent, edging a first-set tiebreak and breaking late in the second set to seal the match.
The two players have had a rocky relationship.
Tensions flared between them in Miami last year and Tsitsipas recently labeled Medvedev's way of winning as "boring" after defeat against the Russian in Shanghai.
The Greek player said Medvedev had got "into my head" in Miami – he said the row had centered on a demand from the Russian for an apology over a net cord.
"I mean, our chemistry definitely isn't the best that you can find on the Tour," said Tsitsipas, who added that Monday's match had been tougher because he was so desperate to win.