Nootbaar has been out since suffering a lower-back contusion when he crashed into the outfield fence on May 29.
Nootbaar, 25, went 4-for-5 with two home runs and four RBIs on Sunday in his final rehab game for Triple-A Memphis.
He is batting .266 with four homers and 21 RBIs in 42 games in the majors this season.
The Cardinals optioned first baseman Luken Baker to Memphis in a corresponding transaction.
Baker, 25, made his MLB debut on June 4 and went 4-for-14 with five strikeouts in four games.
Naughton hasn't pitched since April 7, when he left a game against the Milwaukee Brewers after just two-thirds of an inning, reporting left forearm tightness.
Cardinals manager Oliver Marmol said the surgery will be performed June 26, but he didn't state the specific surgery type. It isn't known yet whether Naughton will be available at all in 2024.
Last week, Naughton began a rehab assignment with Triple-A Memphis but was pulled after throwing just three pitches when he reported feeling something "tug" in his arm.
The 27-year-old Naughton made his career debut with the Los Angeles Angels in August 2021 and joined St. Louis before the 2022 season. With the Cardinals, he has appeared in 30 games (three starts), tallying a 0-2 record with a 4.14 ERA. He has one save in 37 innings, with 36 strikeouts and eight walks.
With the Angels, he was 0-4 with a 6.35 ERA in seven games (five starts).
Reuters contributed to this report.