The All-Star goalie planned to return Tuesday from Massachusetts but will instead come back to the team Wednesday.
Since DiPietro didn't play Sunday during the Islanders' loss to Florida or practice with the team on Monday or during Tuesday morning's pregame skate, general manager Garth Snow told the franchise goalie to take another day with his family.
DiPietro, 26, left immediately after the Islanders' home loss to Philadelphia on Saturday.
"He had a wake Sunday and a funeral on Monday," Snow said. "It didn't make sense [to rush back to play]. I promise you he's not hurt. As much as he wanted to play, I didn't think it was right.
"He's gone through a traumatic experience. I anticipate he'll start Thursday, but that's a coach's decision," he said.
Wade Dubielewicz played in DiPietro's place on Sunday and made 29 saves, when New York lost 1-0 to Florida despite recording 53 shots. He started again against the Rangers on Tuesday night, making 27 saves through overtime and then turning aside five in a shootout in a 4-3 win.
"It's just an unfortunate thing happening with his family, so he is going to take care of that first," Islanders coach Ted Nolan said. "Dubielewicz played quite well for us last time so we'll go with Dubie."
DiPietro, 25, is expected to be at practice on Wednesday and will be available to play on Thursday when the Islanders and Rangers complete a home-and-home series on Long Island.
However, Nolan wouldn't commit to going back to DiPietro, in the second season of a 15-year contract with New York, for the Rangers rematch.
"It depends on here tonight," Nolan said before the game. "Right now, we're in the business to win some hockey games, and Ricky hasn't seen the ice in three or four days now. We'll see how he responds at the next practice [Wednesday] and see how Dubie plays tonight."
There was no guarantee that DiPietro would have played Tuesday had he returned to the team. Nolan said he would've given "strong consideration" to starting Dubielewicz, regardless.
The Islanders were again without defenseman Bruno Gervais, who sustained a concussion and a bruised thigh Sunday when he took a high, hard check from Florida's Branislav Mezei late in the first period.
Gervais was injured in the first period and didn't return to the game.
"He got re-evaluated, but it's still kind of iffy," Nolan said.
Defenseman Aaron Johnson rejoined the Islanders lineup Tuesday night against the Rangers.