With the game tied at 1-1, the tarp was brought onto the field before the bottom of the second inning got underway.
The game was postponed over an hour later after it was determined the rain was not going to stop.
The contest will pick up where it left off Saturday at 8:37 p.m. (et), and Game 2 will be played on Sunday at 3:07 p.m.
But the Yankees tied the game in the home first. Derek Jeter struck out, but advanced to first on a Justin Verlander wild pitch. Curtis Granderson followed with a walk. The runners advanced a base on Robinson Cano's groundout. Alex Rodriguez followed with an RBI groundout to make it 1-1.
Sabathia retired the side in order in the top of the second.
The Yankees are back in the postseason for the 16th time in the last 17 years after winning their 12th American League East title over that span. They enter this year's playoffs with more wins than any team in the American League at 97.
The Tigers won their first-ever American League Central title, while claiming their first division crown since winning the 1987 AL East.
The Yankees and Tigers have met just once in postseason play, with the Tigers winning the 2006 ALDS.