Burnett, who had a 5.26 earned run average and a 10-15 record during the regular season, was not on the roster for New York's three-game sweep of the Minnesota Twins in the division round.
As expected, CC Sabathia will get the start when the Yankees open the ALCS Friday at Texas. Phil Hughes, who pitched in the third game of the division series, will be moved up to No. 2 starter against Texas and Andy Pettitte will start Game 3 Monday in New York.
Burnett made five playoff starts in 2009 and had a 1-1 record with a 5.27 ERA. Both the decisions came in the World Series.
Potential long relievers Dustin Moseley and Sergio Mitre were kept on the New York roster for the ALCS. Veteran starter Javier Vazquez was dropped from the roster.
Texas will start C.J. Wilson in the opening game of the best-of-seven series. He won the second game of the eventual five-game triumph over Tampa Bay.