Santander has been one of the best players on a rebuilding team that has performed above expectations following two straight 100-loss seasons. With Saturday's 6-1 win over the Yankees, the Orioles improved to 18-21.
Santander suffered the injury in the opener of a doubleheader against New York on Friday.
"When he came out of the game, that didn't look good," manager Brandon Hyde said. "That one definitely hurt."
With three weeks to go in the abbreviated 60-game schedule, the Orioles are bracing for finishing without Santander, who was batting .261 to go with his team-leading 11 homers and 32 RBIs.
"It's definitely a possibility," Hyde said. "Really happy with the year he's had. It's a huge loss for us and he's very disappointed."
Santander, 25, broke into the majors with Baltimore in 2017. He has a career batting average of .252 with 32 home runs (including 20 last year) and 99 RBIs.
Hyde said DJ Stewart will get the majority of playing time in right field. Stewart, who was 0-for-16 coming into Friday's game, homered twice for his first two hits of the season.
In addition to placing Santander on the 10-day IL, the team selected the contract of outfielder Mason Williams from its alternate training site. Pitcher Evan Phillips was optioned to the alternate site with right-hander David Hess recalled to fill Phillips' roster spot.
The Associated Press contributed to this report.