Kwan will be placed on the injured list Monday, Zack Meisel of The Athleticreports.
Kwan (hamstring) is out of the lineup for Sunday's game against the Angels.
Kwan was lifted from Saturday's game against the Angels due to left hamstring tightness, Zack Meisel of The Athletic reports.
Kwan went 3-for-5 with a triple, a double and two RBI in Wednesday's 3-2 extra-inning win over the Astros.
Kwan went 1-for-4 with a solo home run in Friday's 6-2 loss to Atlanta.
Kwan is absent from the lineup for Thursday's contest in Boston.
Kwan went 3-for-5 with a walk and two runs scored in Tuesday's 10-7 extra-innings win over the Red Sox.
Kwan went 2-for-5 with a solo home run in Wednesday's 6-5 extra-inning win over the White Sox.
Kwan went 3-for-5 with three runs scored in Wednesday's 8-0 win over the Mariners.
Kwan went 3-for-5 with a solo home run, a walk, two RBI and three runs in Saturday's 12-3 win at Oakland.