Yankees vs. Teams other than the Twins (0-4)
2002 Lost to Angels (3-1)
2005 Lost to Angels (3-2)
2006 Lost to Tigers (3-1)
2007 Lost to Indians (3-1)
Does this mean anything? This encompasses two different managers over a long period of time. Joe Girardi has not lost in the first round, and Joe Torre only started in in his last few seasons with the Yankees. Maybe they would have lost to the Twins if they played them in 2005-2007, or maybe not.
This probably won't be weighing on the Yankees like the Curse of the Billy Goat might on the Cubs, but they are surely aware that the Yankees haven't beaten anyone in the first round other than the Twins since 2001. The 2001 team that beat the A's had Paul O'Neill, Bernie Williams, Tino Martinez and Scott Brosius, and was the last hurrah of the dynasty that had won the previous three World Series.
This team is obviously very talented and dangerous, but they are relying to some extent on pitchers that have seen better days (Bartolo Colon, Freddy Garcia, A.J. Burnett). Will they be able to hit Verlander, Fister and Scherzer? They might, although they've been shut down before (they scored only 13 runs over the final 5 games of the 2010 ALCS against the Rangers, with 7 coming in one game).
The Tigers are likely to be a good matchup for the Yankees, who will try to win an ALDS against someone other than the Twins for the first time in 10 years.