Jack Jamisson Kinsler weighed in at 6 pounds, 9 ounces, and mother and child are doing well.
The Rangers called up infielder Chris Davis from Triple-A Round Rock.
Under MLB's paternity leave rule, which went into effect this year, teams can call up a replacement for 24 to 72 hours.
The plan is for Kinsler to rejoin the team in Minnesota on Friday. The Rangers play the Detroit Tigers on Wednesday night and start a road trip against the Twins on Thursday.
This is the second time the Rangers have used the new rule. Pitcher Colby Lewis, who's wife had a child in mid-April, was the first major leaguer to go on paternity leave.
"We have a fertile club," joked general manager Jon Daniels.
Kinsler had five hits in the first two games of the current three-game series against the Tigers. That came after he slumped on a seven-game road trip, going just 1-for-22.
He's hitting .235 with seven homers and 23 RBIs and was was third among AL second baseman in the most recent All-Star balloting.
Richard Durrett covers the Rangers for ESPNDallas.com.