Adam Kilgore of the Washington Post noted the designated hitter rolled his ankle at second base and the injury looked "real bad."
Encarnacion is one of Major League Baseball's top sluggers, and he was a key acquisition for the Tribe during the offseason.
In the midst of his first season in Cleveland, Encarnacion produced to the tune of a .377 on-base percentage with 38 home runs and 107 RBI during the regular season.
The 34-year-old veteran entered 2017 having hit at least 34 home runs and driven in at least 98 runs in each of the previous five campaigns, including a .263 batting average, 42 jacks and an American League-best 127 RBI in 2016 for the Toronto Blue Jays.
Encarnacion was part of one of the most fearsome power-hitting lineups in baseball during his time with the Jays, and he is currently the centerpiece of Cleveland's offensive attack.
While the Dominican Republic native doesn't have a history of significant injuries, he has dealt with his fair share of bumps and bruises in recent years.
Prior to appearing in 160 games last season, Encarnacion missed double-digit games in each of his first six full seasons in Toronto.
There is no replacing a hitter of Encarnacion's caliber; and Cleveland doesn't possess a ton of pop off the bench. If Encarnacion is forced to miss an extended period, Lonnie Chisenhall, Austin Jackson and Michael Brantley could all see some extra playing time during the postseason.
While that would put Cleveland at a significant disadvantage in comparison to its usual lineup, the Indians have a strong pitching staff that should at least keep them competitive in the meantime.