The sides were due to meet in a fourth-versus-second televised clash, but referee Keith Stroud took the decision to call the game off this morning.
The Blades confirmed the cancellation on their official Twitter feed.
Elsewhere in South Yorkshire, the race meeting at Doncaster was abandoned for the same reason.
The fixture was due to feature the first major event of the Flat season, the William Hill Lincoln, but clerk of the course Roderick Duncan called off the card following a 6am inspection.
He said: “We have had about two to three inches of snow overnight and it’s still falling now.
“Daytime temperatures are forecast to stay at or below freezing and further snow is forecast today.
“The meeting will now switch to next Saturday (March 30) after contingency plans to transfer the meeting were agreed on Thursday.
The meeting at Newbury was the next to go, with the fixture abandoned because of snow.
Clerk of the course Richard Osgood found the track fit to race on first inspection this morning, but called a further check for 10am as snow was starting to fall.
He now reports the snow to be falling heavily and the course is unraceable.
Osgood said: “We have had to call it off. We’ve taken a lot more snow than we expected and it’s still coming down now.”All we can see right now is snow and the course is unraceable.”
Another League One clash, Shrewsbury’s home meeting with Oldham, quickly followed the Sheffield postponement, with the home side confirming on their website that snow had taken a hold.
In League Two, Port Vale’s home meeting with Aldershot was also wiped out, with groups of fans unable to clear the pitch as snow continued to fall. Vale acknowledged the postponement on their website.
Tomorrow’s race meeting at Wincanton, though, was given the go-ahead.
“We have just showers forecast today and tomorrow now and we are not planning any further inspections,” said clerk of the course Barry Johnson.
“However, we will be keeping an eye on the weather as it is snowing at Newbury and while that is not forecast to get as far as us, we will be monitoring the weather.”