Murakami went 1-for-3 with a solo home run in Wednesday's loss to the Pirates.
Smith will start Thursday's game against the Pirates, James Fegan of the Chicago Sun-Times reports.
Montgomery got the save Wednesday against the White Sox, striking out two in a scoreless ninth inning.
Valdez went 1-for-2 with a solo home run in the win Wednesday against the White Sox.
Griffin went 1-for-4 with two RBI and two stolen bases Wednesday in the 4-2 win over the White Sox.
Martin (9-7) took home the loss Wednesday against the Pirates, allowing one run on four hits and two walks. He struck out one.
Vargas is absent from the lineup for Wednesday's tilt against the Pirates.
The White Sox placed Davis on the bereavement list Wednesday.
Horwitz went 3-for-5 with three RBI in Tuesday's 9-3 win over the White Sox.
Burke (8-7) took the loss Tuesday against the Pirates after allowing seven runs on eight hits and two walks while striking out two over 1.1 innings.
