McClanahan (forearm) will not return before the conclusion of the regular season, Marc Topkin of the Tampa Bay Times reports.
Simpson went 1-for-3 with two RBI and a stolen base in Sunday's 5-1 win over the Red Sox.
Brown took a no-decision Sunday against Atlanta, striking out while allowing three hits and two walks in five scoreless innings.
Jax (8-10) earned the win against the Red Sox on Sunday, allowing three hits and two walks while striking out five over five scoreless innings.
Altuve went 2-for-4 with a solo home run Sunday in a 4-2 loss to Atlanta.
Tampa Bay designated Fraley for assignment Sunday.
Tampa Bay reinstated Williamson (hamstring) from the 10-day injured list Sunday.
Lambert (8-10) took the loss Friday against Atlanta after allowing two runs on six hits and a walk while striking out six across 5.1 innings.
Seymour (9-7) was tagged with the loss against the Red Sox on Friday, allowing four runs on seven hits and two walks while striking out five across five innings.
Cleavinger (forearm) is expected to resume mound work Saturday, MLB.com reports.
