Hudson was a perfect 2-0 with a 1.80 ERA in 15 innings of work, earning wins against division-rival San Diego and an Interleague victory against the Twins.
He shares the honor with Brewers starting pitcher Shaun Marcum.
Hudson, 24, racked up 12 strikeouts in the two outings, while walking just two. He scattered eight hits over seven innings at Chase Field on Tuesday against the Padres, and pitched eight shutout innings against the Twins on Sunday in his first Interleague start.
Hudson struck out six without a walk on Sunday, helping the D-backs to a three-game sweep of the Twins.
Hudson has gone at least six innings in nine of his last 10 starts.
It is the right-hander's first career weekly award. The D-backs, winners of six in a row, are back in action Tuesday afternoon against the Rockies at Coors Field.