Davis hit .423 (11-for-26) with five home runs and 10 RBIs last week for the Orioles, who clinched their first playoff berth since 1997 on Sunday night. Davis led all AL players in homers, RBIs, total bases (27) and slugging percentage (1.038) while finishing second in runs scored.
The 26-year-old's biggest day came Wednesday, when he had two homers and drove in five runs in a 12-2 victory over the Blue Jays. He also went deep in each game of Baltimore's weekend series against Boston, including a two-run shot in Friday's series opener.
This marks Davis' first career weekly award.
Verlander, meanwhile, capped his quest for a second consecutive AL Cy Young Award by going 2-0 with a 1.20 ERA. He struck out 16 in 15 innings to bring the Tigers' AL Central-clinching magic number to one entering Monday.
The 29-year-old right-hander held the Royals to two runs and struck out eight in eight innings Monday before allowing an unearned run in seven innings against the Twins while striking out eight. It is Verlander's sixth career weekly award.
Also considered for the award were two of Verlander's teammates, first baseman Prince Fielder and righty Anibal Sanchez. Fielder hit .346 with three homers, while Sanchez tossed a shutout against Kansas City on Tuesday.