The teams will make up the game at 4:05 p.m. ET Tuesday, with gates opening at 2 p.m.
The Phillies and Mets are set to play Tuesday night and Wednesday afternoon. Rain is in the forecast both days.
Yankees manager Aaron Boone said he still plans to start left-hander Jordan Montgomery in the makeup game. Boone said he and pitching coach Larry Rothschild had considered moving Wednesday's starter Luis Severino up a day, but they decided to stick with Montgomery, who will be making his season debut.
Tampa Bay will counter with Chris Archer, moving the righty up one day from his previously scheduled Wednesday start. Archer earned a no-decision Thursday against the Boston Red Sox, allowing four runs and six hits with six strikeouts in the Rays' 6-4 win.
Official word of Monday's postponement came about four hours before the originally scheduled 1:05 p.m. ET first pitch, with a couple inches of snow sitting on the field.
Tuesday's game will be Boone's first as a manager at Yankee Stadium.
"I'm looking forward to putting the pinstripes on and walking out on the field with this team," the former Yankees player said.
When Boone looked out the window at home Monday morning, he was pleasantly surprised, like many in the region.
"Huh," he said, recalling his thoughts while looking out the window, "it really is a 100 percent chance of snow at 7 a.m.
"I thought, 'This is going to be interesting.'"
Forecasts had called for at most 3 inches of snow that would clear mid-morning. As of 10 a.m. ET, LaGuardia Airport reported 5.5 inches, according to the National Weather Service.
The postponement also means that Yankees fans eagerly awaiting to see Giancarlo Stanton don pinstripes for the first time in a regular-season game will have to wait one more day.
"It'll be some extra anticipation," Stanton said. "It's going to be fun. The atmosphere, hitting here, I've only had two games here. So I'm looking forward to it."
Stanton's home opener last season looked and felt dramatically different. Against the Atlanta Braves on April 11, the Miami Marlins played in climate-controlled Marlins Park. On the outside, it was 81 degrees.
Traded to the Yankees in the offseason, Stanton went 2-for-8 with an RBI and a run scored in his only games at Yankee Stadium while with the Marlins. He was named last year's National League MVP after hitting a major-league-leading 59 home runs.
Brought to New York because of his bat, Stanton, the right-handed hitter who spent spring training battering balls off the right-field wall and hitting a few out to center and right-center, believes his swing is well suited for Yankee Stadium. The ballpark features a shorter distance down the right-field line (314 feet) than most big league venues.