Markakis hit .429 (6-for-14) with two doubles, two home runs, four RBIs and five runs scored in the shortened week ending on July 17.
It is Markakis' first career AL Player of the Week honor and the first time a Baltimore player has won the award since Luke Scott on July 25, 2010.
During Friday's 6-5 loss to the Indians, Markakis knocked his 1,000th career hit with a third-inning single to become the 14th player to reach the plateau while with the Orioles.
Markakis then went 3-for-4 with two doubles, a homer and three runs scored on Saturday to help the Orioles beat the Indians, 6-5.
It was the third time in Markakis' career that he went for three extra-base hits in a game and the first occasion since 2008.
Entering Monday, Markakis has hit .333 (13-for-39) with two doubles, two home runs and seven RBIs over a 10-game hitting streak.