The moves were made before Monday night's series opener against the Los Angeles Angels.
Jackson was injured in Sunday's loss at Houston when he stepped on pitcher Roberto Hernandez's foot at first base while running out a ground ball. He is batting .242 with two homers and four RBIs in 25 games.
Beimel signed a minor league contract with Seattle on April 2, and began the season on extended spring training before joining the Triple-A Rainiers and making three appearances without allowing a run. He was 3-1 with a 2.20 ERA in 56 appearances last season with the Mariners.
Taylor began the season on the disabled list with a fractured right wrist before he was activated and optioned to Tacoma on April 18. He batted .313 in 21 games with the Rainiers.
Kickham, acquired in a trade with the Chicago White Sox on Jan. 14, was 0-2 with a 7.29 ERA and a 28-to-12 walk-to-strikeout ratio in five starts in Triple-A.