He was taken to New York-Presbyterian Hospital and diagnosed with a low-grade left calf strain.
With Tulowitzki on the injured list, the team recalled infielder Thairo Estrada from Triple-A.
The Yankees entered play Thursday with a record of 2-4. They have a league-high 11 players on the injured list.
New York inked Tulowitzki as a free agent for the major league minimum of $555,000 to fill the void for injured shortstop Didi Gregorius.
"I've never seen anything like it," Tulowitzki said to The New York Times about the number of players New York has on the injured list.
Tulowitzki missed the entire 2018 season following surgery. In five games this season, he is hitting .182 (2-for-11) with one home run and one run batted in.
He went on the injured list July 29, 2017, with a sprained right ankle. He had surgery on both heels in March 2018 that kept him out for all of last season.
"We've hit a little bit of adversity here with some of the injuries we're dealing with," Yankees manager Aaron Boone said via MLB.com, "but I'll hang my hat on our group and know that we'll fight our way through this."