La Russa said he received a text message announcing the births Tuesday afternoon. La Russa said during his pregame chat that McGwire wrote that his triplets are "doing awesome" and that "Steph is great," according to the St. Louis Post-Dispatch.
La Russa said after Monday's 12-4 victory over the Cincinnati Reds that it was McGwire's last day with the team for a "day or two." La Russa said McGwire got a round of applause in the clubhouse after the game.
McGwire's wife, Stephanie, is from Glen Carbon, Ill., near St. Louis, and the family is living there during the season.
During McGwire's absence the team's second hitting coach, Mike Aldrete, will likely take on added responsibility.
The 46-year-old McGwire now has five children in his second marriage.
Information from The Associated Press was used in this report.