The Wildcats were up 38-17 in the third quarter when Morrison returned the punt to extend Arizona's lead to 45-17. Morrison's 63-yard return was the longest of his career and Arizona's first punt return for a touchdown since November 7, 2009.
The award is Arizona's third Special Teams Player of the Week honor this season.
Morrison has 23 receptions for 171 yards and two touchdowns for the 4-3 Arizona Wildcats this season.
Arizona's win over Washington ended a three-game conference losing streak as the Wildcats lost to Oregon, Oregon State and Stanford in consecutive weeks.
The Wildcats will attempt to win two games in a row when they host No. 9 USC this Saturday. The Trojans defeated the Wildcats, 48-41, in last year's meeting.