Almonte, 24, hit .297 with six home runs for Triple-A Scranton/Wilkes-Barre. Warren, 24, has pitched 34-2/3 innings for the Yankees already this season, and has an ERA of 3.12.
Youkilis, who was signed to replace third baseman Alex Rodriguez, has hit .219 with two home runs this season in 118 plate appearances.
The team will go with David Adams and Laynce Nix as their fill-ins at third base, and without many prospects to trade or options to target, they will likely not be able to find much on the trade market.
The team has been hit with a dizzying array of injuries this year, with Youkilis' being the latest. Despite their high payroll, the Yankees are in just third place as they near the All-Star break.
Unlike some of their other injuries, the Yankees do not have any long-term money invested in the 34-year-old infielder, so they do not have to worry about his long-term health.