The Angels placed Trout on the list Thursday and recalled right-handed pitcher Kyle Keller from their alternate training site in a corresponding translation.
Trout, 28, and his wife, Jessica, announced in March that they expected to have a baby boy in August. The baby's due date is Monday. The Angels face the Houston Astros Saturday and Sunday in Anaheim, Calif.
Trout hit .292 with a home run and four RBIs in the Angels' first six games before he missed the team's 8-5 loss to the Seattle Mariners Thursday in Anaheim. Keller allowed two hits and a run in two-thirds of an inning for the Angels.
Trout won his third MVP award last season after he hit .291 with a career-high 45 home runs and 104 RBIs. He led the American League with a .645 slugging percentage and led baseball with a .438 on-base percentage in 2019.
Trout will continue to take daily COVID-19 tests during his absence. He can return to the Angels without a quarantine as long as he continues the tests.
The Angeles star voiced hesitation about his participation in the shortened 2020 MLB season before the season began, citing safety concerns for his family. He still reported to the Angels in time for the team's season debut.
The Angels host the Astros at 7:07 p.m. EDT Saturday at Angel Stadium.