The Royals entered action Monday four games back of the second AL Wild Card spot.
Morales, 33, posted two multihit games last week, including a two-homer performance in Kansas City's 10-3 romp of Minnesota on Tuesday. He also knocked out three hits the following day in a 6-5 loss.
Morales closed the week with a solo homer in Sunday's 2-0 win in Chicago.
This is Morales' fourth career weekly honor and second of the season, the other coming for the week of July 3.
Cash Kruth is a reporter for MLB.com. Follow him on Twitter at @cashkruth. This story was not subject to the approval of Major League Baseball or its clubs.