Meanwhile, Akinori Iwamura's suspension hearing was moved from Tuesday to Wednesday.
Once Bartlett returns, Zobrist will likely move to second base to play in Iwamura's absence, unless Carlos Pena is activated, which would mandate a roster move. In the event of Pena returning before Iwamura, Willy Aybar could play second base.
The Rays optioned Zobrist to Durham on May 30 and he sprained his right shoulder while playing for the Bulls. He played just four games at Durham before getting recalled on Monday.
"I felt like my timing is pretty good, even though I haven't swung a lot," Zobrist said. "My shoulder's feeling healthy. I'm ready to play shortstop or whatever, when Bartlett needs to go be with his wife. I'll just fill in wherever I'm needed."
Rays manager Joe Maddon would not say how long Zobrist will be with the team.
"Of course, it's based on [Bartlett] leaving and Aki leaving," Maddon said. "We'll see how it plays out. There's no reason he has to go away at some point. We'll see how it plays out in the next couple of days. And then, of course, Pena is coming back and a move will have to be made."
Bartlett said he would have his telephone on during Tuesday night's game and will return to St. Petersburg if Kelly goes into labor. Tateki "Bori" Uchibori, who serves as Iwamura's translator, will monitor Bartlett's phone during the game.
The Bartletts are having a boy and Jason said the couple plans to name him Jayden Anthony Bartlett.
"I think about [the birth] all day and I check my phone a lot, just to make sure everything is OK," Bartlett said. "When the game's going on, I'm thinking about the game and as soon as I get back in the clubhouse, I think about that."
Meanwhile, Maddon would like to hear some good news regarding Iwamura's appeal.
"You have to have a reason to appeal, and hopefully we'll get it reduced," Maddon said.