The Rays also got third baseman Matt Sweeney and a player to be named later in the deal made late Friday.
It appears to be a red flag from the Rays on their chances to qualify for this season's American League playoffs.
They won the AL pennant in 2008 for the first time in franchise history.
Kazmir (8-7) is Tampa Bay's all-time leader in wins (55), innings pitched (834), strikeouts (874), starts (14), and quality starts (71), despite being just 25 years old.
The Houston native was selected 15th overall in the 2002 Major League Draft by the New York Mets.
Copyright 2009 by United Press International.