Voit, 28, left Tuesday's 4-2 loss to the Arizona Diamondbacks with the injury. He missed seven games earlier this month with an abdominal strain.
Boone said he expects the Yankees to know more about Voit's prognosis Thursday.
Voit was placed on the 10-day injured list Wednesday morning. Yankees recalled infielder Breyvic Valera from Triple-A Scranton Wilkes-Barre.
Voit is hitting .278 with 19 home runs and 54 RBIs in 94 games this season. Edwin Encarnacion is expected to start at first base in Voit's absence.
New York also placed pitcher David Hale on the injured list with a back strain. Reliever Jonathan Holder was recalled from the Triple-A Yankees to fill Hale's spot in the bullpen.
New York entered play Wednesday with a 67-39 record. The first-place Yankees have a 7 1/2 game lead over the Tampa Bay Rays in the AL East Division.