Seton Hall was leading 56-47 with 13:03 remaining when play was stopped for good by game officials Tim Clougherty, Jeff Anderson and James Breeding.
The game will be finished at noon Thursday at Alumni Hall on the Friars' campus (The Dunk is off-campus) with the same three referees. Because of the small capacity of Alumni Hall, only Providence students and faculty will be admitted into the game.
"At the end of the day, as disappointed as the fans were, it was the right decision," Friars athletic director Bob Driscoll told ESPN.
Seton Hall is 18-9 and 7-7 in Big East play and was projected as a No. 9 seed in the NCAA tournament by ESPN's Joe Lunardi entering Wednesday night's games. Providence is 17-10 overall and 8-6 in league play and was projected as a No. 10 seed.
"As big of a game [as] this is, the kids' careers are more important," Seton Hall coach Kevin Willard said.
"This game is huge for both teams," Friars coach Ed Cooley said. "But the decision not to play on a slippery floor was the right one. Player safety is more important than the game."
The tipoff will allow Providence to still make its flight at 5:20 p.m. ET Thursday to get to Washington for its Friday game at Georgetown.
Seton Hall's Desi Rodriguez suffered an ankle injury slipping on the floor in the first half Wednesday. Coach Kevin Willard said Rodriguez is likely to miss about a week.
"It was real slippery," Seton Hall's Angel Delgado told ESPN. "Two of my teammates got hurt. Coach puts us before anything else."
Driscoll said that the combination of the warm weather outside and the ice underneath the court contributed to the condensation on the court.
Providence last played at Alumni Hall in its season opener against Houston Baptist. Before that, it was March 1, 1972.
Those in attendance Wednesday who aren't permitted to attend Thursday because of the arena's small capacity will have the opportunity to redeem tickets to select Big East games next season once the schedule is released in September.