Arcia, an outfielder, has a hip flexor strain.
The team called up 23-year-old prospect Eddie Rosario to replace Arcia in the outfield.
Arcia, 23, was hitting .276 with two home runs in 65 plate appearances before the injury. In 2014, he batted .231 with 20 home runs.
Rosario had been hitting .242 at Triple-A Rochester. He entered the season as the Twins' No. 9 prospect, according to MLB.com.
The Twins are 13-12 on the season, good for third place in the AL Central.
- Alex Putterman