Murray also withdrew from next week's ATP Toronto Masters, citing the drain from three gruelling three-set victories over more than eight hours on the U.S. capital hardcourts. The top-seeded German is looking to become the first back-to-back victor of the hard-court U.S. Open tuneup since Juan Martin del Potro in 2008 and 2009.
"It's like playing two matches in a day". I know that the weather's tricky for the scheduling.
I don't think I should be put in a position like that.
Murray is working his way back into form after having surgery on his right hip and being sidelined for 11 months. It's not good for the players, not good, I don't think, for anyone involved in the event.
Murray said: "Sadly, I won't be able to take my place in the draw in Toronto".
The 19-year-old Tsitsipas is coming off his first run to the fourth round at a Grand Slam tournament, last month at Wimbledon. "It's a handsome thing to see", he said. Zverev joked after advancing, "I think I'm the only one that's allowed to buy a drink in the US, right?" "And I'm disappointed with that, because I know that the weather's tricky and I know it is for the scheduling, but it's a very hard position to be in".
With storms forecast to return about the time Murray's match would start, he could face an early quarter-final and late semi on Saturday.
Tsitsipas reached his first career ATP final in May at Barcelona, losing to Rafael Nadal.
Germany's third-ranked Zverev, seeking his fifth final of the season and third title of the year after Munich and Madrid, dispatched seventh-seed Nishikori, the 2015 champion, as he did in last year's Washington semi-finals.
Britain's former world number one Andy Murray says he may not play his Washington Open quarter-final after sealing his third-round victory at 03:02 local time.
On the women's side, two-time Grand Slam victor Svetlana Kuznetsova was to face Kazak eighth seed Yulia Putintseva for a semi-final spot.
The frustrations included Murray leading the first-set tie-breaker 5-0 only to drop the next seven points and the set.
The match eventually finished at 3am on Friday morning and Murray shed tears into a towel for several minutes courtside as the emotion of the moment overcame him.