The 35-year-old goaltender signed a one-year contract with Detroit on Thursday.
Nabokov, who played with the San Jose Sharks for parts of 10 seasons, had spent this season with SKA St. Petersburg of the Russian KHL and hadn't yet played for Detroit.
The NHL's collective bargaining agreement states that anyone who plays in a professional league before signing an NHL contract must clear waivers.
Once he signed his one-year deal with the Red Wings, he became available to the Islanders.
New York owns Nabokov's rights and could keep him out of the NHL for all of next season should Nabokov not report.
Nabokov has been disappointed that he won't be joining the Stanley Cup-contending Red Wings. Instead he is now under contract with the Islanders, who are far out of the Eastern Conference playoff race.
The Islanders had little to say about Nabokov after a 1-0 loss to the Penguins in Pittsburgh.
"I'm just a coach — we try to prepare our team to win the game. That's for our general manager, obviously, to make the decisions that he makes," coach Jack Capuano said.
New York entered Tuesday with the third-worst goals-against average (3.20) in the league.
"I don't know what will happen with that situation, but it's not something we're worried about," rookie defenseman Dylan Reese said. "We're worried about getting wins right now, and if he comes, he comes and if he doesn't, he doesn't."
Rookie goalie Kevin Poulin — who likely would have been sent back down to the American Hockey League had Nabokov reported — was strong Tuesday night in Pittsburgh, stopping 30 of 31 shots.
"He didn't come," Poulin said of Nabokov, "so too bad for him."