Saunders and his wife, Jessica, have a home in Castle Rock, Colo.
Manager Eric Wedge said Saunders flew home after Sunday's game and the baby was born Tuesday. Though Saunders was penciled in at right field in the initial lineup for Tuesday's game, he was replaced by Eric Thames several hours before game time.
Wedge said he wasn't sure yet when Saunders would rejoin the team.
"We'll just communicate and play it by ear," Wedge said. "I'll talk to him again later tonight or early tomorrow."
Saunders is the third Mariners player to have a baby in the last two months, joining Mike Carp and Tom Wilhelmsen.