The 22-year-old is 1-1 with a 1.23 ERA in 15 relief appearances for Triple-A Scranton/Wilkes-Barre, striking out 29 in 22 innings.
Lindgren was selected by the Yankees in the second round of last year's amateur draft with the 55th overall pick.
New York transferred shortstop Brendan Ryan to the 60-day disabled list before Sunday night's game. The Yankees opened a spot on the active roster by optioning right-hander Branden Pinder to Scranton after he threw 48 pitches over three innings in Saturday's 15-4 loss. New York lost 10-9 to Texas on Friday night.