The move is retroactive to Saturday.
In other moves, the Guardians selected the contract of outfielder Myles Straw from Triple-A Columbus and made room for him on the 40-man roster by designating right-hander Carlos Carrasco for assignment.
Kwan, 27, hasn’t played since Thursday and missed four starts before he was placed on the IL ahead of Tuesday’s home game against the Minnesota Twins.
He is batting .291 with 13 home runs and 43 RBIs in 120 games and has career bests in slugging percentage (.419) and OPS (.783) this season.
He is eligible to return Sept. 24 against the Cincinnati Reds, when the Guardians have five regular-season games remaining. They entered Tuesday leading the AL Central at 87-64, five games ahead of the second-place Kansas City Royals.
Carrasco, 37, was 3-10 with a 5.64 ERA, 33 walks and 89 strikeouts in 103 2/3 innings over 21 starts before he was placed on the 15-day IL with a hip strain.
He is a career 110-103 with two saves and a 4.14 ERA in 324 games (277 starts) with Cleveland (2009-11, 2013-20, 2024) and the New York Mets (2021-23).
Carrasco was the 2019 AL Comeback Player of the Year award and the 2019 Roberto Clemente Award winner.
Straw, 29, was batting .240 at Triple A with three homers and 47 RBIs in 123 games. He last played for Cleveland in 2023, batting .238 with one homer and 29 RBIs in 147 games.