The game will be played at 8 p.m. ET Tuesday and nationally televised by NBC.
Philadelphia Mayor Michael Nutter declared a snow emergency as of 2 p.m. ET Sunday.
In announcing the postponement of the game, NFL spokesman Greg Aiello said: "Due to public safety concerns in light of today's snow emergency in Philadelphia, tonight's Vikings-Eagles game has been postponed. Because of the uncertainty of the extent of tonight's storm and its aftermath, the game will be played on Tuesday night at 8 p.m. This will allow sufficient time to ensure that roads, parking lots and the stadium are fully cleared. The National Weather Service states that a winter storm warning in Philadelphia remains in effect until 1 pm on Monday."
The Vikings decided against flying back to Minnesota on Sunday and instead will stay in Philadelphia until Tuesday.
"It's tough, especially in a season that you didn't think any more curveballs could happen," kicker Ryan Longwell said. "This is a rough one being away from our families during Christmas and being stuck in Philly. At the same time, you realize that you've got to reconfigure the mind for Tuesday night and show up ready to play."
For some players, the postponement offered more time to rest and heal.
"Hey, at least it's another couple of days to heal," said Vikings running back Adrian Peterson, who's questionable because of a knee injury that kept him out of the Bears game. "We just have to handle this like we have everything else that has gone on this season. Coach (Leslie) Frazier told us to continue to stick together, to stay focused, and that's what we'll do. This is just another bump in the road."
"We'll be off Wednesday, then we'll come back Thursday and do a little more (than a normal Thursday), then we'll have a normal Friday, bring them to the hotel Saturday, and go Sunday."
NBC was uncertain what it would broadcast Sunday night in place of the game, although a spokesman said the regular "Football Night in America" would be on the air from 7 p.m. to 8:30 p.m. ET.
The Associated Press contributed to this report.