Two-time champion Murray went down 7-6(3), (2)6-7, 4-6, 7-6(3), 6-4 after a gruelling four-hour 40-minute match-up.
The defeat means Murray has not made the second week of a Grand Slam since reaching the quarter-finals at Wimbledon in 2017.
It will also raise questions over his long-term future in the sport despite valiant attempts to rebuild his career following two hip surgeries.
"I don't know," said Murray when asked if he would be back at the All England Club next year.
"Motivation is obviously a big thing. Continuing having early losses in tournaments like this don't necessarily help with that."
He admitted that a second round defeat at Wimbledon to John Isner last year had prompted a similar bout of soul-searching.
"I had a long think about things, spoke to my family, decided to keep on going.
"I don't plan to stop right now. But this one will take a little while to get over.
"Hopefully I will find the motivation again to keep training, keep pushing, try and keep getting better."
Tsitsipas fired 90 winners past Murray as he goes on to face Laslo Djere of Serbia for a place in the last 16.
"It's never easy against Andy. Everyone loves him here," said the Greek.
"I'm impressed how well he holds up after his hip surgeries. I wish him the best in the future."
Tsitsipas hailed the influence of Murray as well as fellow Grand Slam heavyweights Novak Djokovic, Rafael Nadal and Roger Federer.
"I had goosebumps when he won his first Wimbledon title," said Tsitsipas of Murray's first Wimbledon title in 2013 which was followed by another three years later.
"I looked up to him, Roger, Novak and Rafa - these four guys shaped the game and they are the reason I am the player I am today."
