Gausman picked up the win in Toronto's 3-1 victory at Tampa Bay on Tuesday. He threw eight innings of one-hit ball with 10 strikeouts and one walk.
He followed that performance with six scoreless innings and five strikeouts in the Blue Jays' 3-2 extra-inning win at Minnesota on Sunday.
It's Gausman's first career player-of-the-week award. He is 8-8 with a 2.91 earned-run average in his first season with Toronto.
St. Louis Cardinals third baseman Nolan Arenado won the National League award after batting .476 (10-for-21) with three home runs and eight runs batted in over six games last week.