He shares the award with Tigers pitcher Justin Verlander, who also went 2-0 this week with two complete-game victories. It is Shields' second weekly award this season.
Shields went 2-0 across two starts, logging 15 strikeouts in a five-hit shutout against the streaking Red Sox and only giving up an unearned run in a victory against the in-state-rival Marlins.
In six games against Florida this year, Shields (7-4, 2.40 ERA) is 2-0 with two complete games, one shutout, 23 strikeouts and one walk.
He has logged a Major League-best five complete games this season, as well as three shutout victories.
The Rays are back in action Monday against the Brewers in Interleague Play.