The Tigers hold a 3-0 lead in the best-of-seven series, which will resume with Game 4 on Thursday at 4 p.m. ET at Comerica Park and televised on TBS.
If necessary, Game 5 will now be held Friday in Detroit on what previously had been a travel and workout day. No start time has been announced for that potential game. If the Yankees stay alive, Games 6 and 7 would remain on schedule for Saturday and Sunday in New York.
Fans holding tickets to Wednesday's game can use those same tickets for Thursday's makeup.
Rain started falling about 90 minutes after the scheduled start time of 8 p.m., and a steady rain fell for hours afterward. Major League Baseball officials said the contest was postponed "in an effort to preserve the integrity of an uninterrupted full nine-inning game."
More rain is forecast for the Detroit area on Thursday morning, but it is expected to clear up completely around noon.
Wednesday's scheduled starting pitchers -- CC Sabathia for the Yankees and Max Scherzer for the Tigers -- will be on the mound Thursday.
"We're baseball players. We're used to getting rained out," Scherzer said. "I'm ready to pitch tomorrow. Nothing changes."
That situation seemingly affects the Yankees more than the Tigers, however, since the thought was that Sabathia could have come back in Game 7 on short rest if the Yankees push the series that far. But Wednesday's postponement eliminates that possibility as he'd now have to pitch on just two days' rest.
But Yankees general manager Brian Cashman said his team can only worry about taking care of business on Thursday and keeping the series going.
"This is a full 25-man roster with a lot of capable guys," Cashman said. "So it doesn't matter what they throw at us, we have to find a way. It's all about winning our next game and then worrying about the day after, the day after. Whatever the schedule turns out to be, it doesn't matter. We will find a way. We have no choice."
Tigers ace Justin Verlander, who won Game 3 on Tuesday, is lined up to pitch Sunday's Game 7 on normal rest, if needed.
Detroit also benefits by getting some rest for temporary closer Phil Coke, who had pitched in the first three games of the series and was told by manager Jim Leyland that he would be held out of Wednesday's contest.
"I was available in my own mind, anyway," Coke said with a laugh. "But this frees up options. It gives everybody an extra day of rest. Obviously it's unplanned and not as much fun as it could have been just because there's no baseball today, as far as we're concerned. But that's the way it played out."
Wednesday's start was delayed even though no rain was falling as officials didn't want to start a game that would have little chance of being completed. A year ago, the Tigers and Yankees lost their aces after an inning and a half in the opener of the AL Division Series in New York under that circumstance.
In that situation, Sabathia and Verlander both started the game, but then were unable to pitch again until Game 3 after the game was postponed in the bottom of the second with the score tied at 1.
Rain in Texas caused a one-day postponement of Game 2 of the ALCS last year between the Rangers and Tigers, when Scherzer was scheduled to pitch for Detroit in that situation as well.
The weather issue was the first of the postseason for the Tigers, who dealt with several delays during their run to the ALCS last year. The Yankees had two rain delays -- but no postponement -- during their ALDS with the Orioles last week, with Game 1 delayed two hours and 26 minutes and Game 2 held up 40 minutes.