Murray and American hope Young were scheduled to be first up on Arthur Ashe Stadium at 11am (4pm BST) on Tuesday but heavy rain has continued to fall in New York and, at just after 1.30pm, tournaments organisers made the decision to call it off.
It had been hoped there would be a window of better weather early in the afternoon but that did not transpire.
A statement read: "The latest forecast indicates worsening conditions with no projected breaks in the rain through the remainder of the day and into the night.
"Due to this forecast, the USTA (United States Tennis Association) is cancelling the Tuesday, September 6 Day Session, and the Tuesday, September 6 Night Session. Play will resume tomorrow, Wednesday, September 7 at 11am, weather permitting."
The worrying news for organisers and players is that the forecast for the rest of the week is poor, with rain expected to prove very disruptive.
The bottom half of the men's draw, which includes Murray and defending champion Rafael Nadal, has been worst hit, with all the other sections having already completed the fourth round.
The news made Roger Federer's speedy victory over Juan Monaco look even more important, with the third seed defying drizzle to win 6-1 6-2 6-0 at 1.13am, not long before the rain set in.
The US Open has been blighted by bad weather in recent years, with the men's final taking place on the third Monday in 2008, 2009 and 2010.
The four remaining men's fourth-round matches will be the priority tomorrow, with Murray, Nadal and Andy Roddick all expected to play first ahead of the women's quarter-finals.
The finalist from the bottom half of the men's singles draw is now almost certain to have to play four matches in five days, giving a major advantage to the likes of Federer and world number one Novak Djokovic.
Much of the talk at the tournament has been about the strains placed on players by the schedule of the season, with a record 14 retirements during matches and four other players failing to make it onto court at all.
Murray has no doubt the demands are too great, and he said: "It's maybe not the length of the season, but there's so many mandatory tournaments you have to play.
"You basically have 16 mandatory events now during the year. It's just too long. And then with Davis Cup, it always comes pretty much the week after the slams. It's quite a long stretch.
"After here, it will be nine weeks since I've been home. That's quite a long stretch, and it happens quite a few different times of the year.
"I just think guys get tired. If you don't look after your body properly and you don't have the right people around you. I'm lucky now to be in a position to have guys with me all the time.
"But when I was younger, it's the same. If you don't have that luxury of being able to have guys, then it's going to be difficult to keep your body healthy throughout the year."
Roger Federer had a different take on the issue, describing the number of retirements as "shocking" and calling on players to think of their responsibility to the fans.
The world number three has never retired during a match while Murray's only incident came in Hamburg in 2007 when he sustained a serious wrist injury against Filippo Volandri and subsequently missed the French Open and Wimbledon.
The 24-year-old believes Federer is missing the point, though, adding: "I think I stopped one match when I couldn't hold a racquet. You've always got to try and give it a go if you can.
"But I'm sure Roger thinks the season's a little bit too long as well. So whether guys are pulling out too quickly or not doesn't change the fact that the season's too long."
A bumper order of play for Wednesday will begin with Nadal facing Gilles Muller on Arthur Ashe Stadium while home favourite Andy Roddick takes on fifth seed David Ferrer on Louis Armstrong.
Murray and Young have been moved to the third show court, the Grandstand, with all three matches taking place at 11am (4pm BST).
The remaining men's fourth-round clash between John Isner and Gilles Simon will follow Murray's match while all four women's quarter-finals and the first two men's quarters are also set to be played, weather permitting.