The Sun Devils went 8-12 in Pac-12 play and finished ninth in the league, a game behind Utah and Colorado.
If BYU wins, it will most likely have to play No. 11 seed Hawaii (24-4) on its home court on Saturday. Hawaii will meet Big Sky Conference champion Idaho State (23-11) on Friday.
Utah, which also made the tournament and will play Yale at Penn State in the first round, swept ASU this season, winning 3-1 in Tempe, Ariz., and 3-2 in Salt Lake City. The Cougars beat Utah 3-2 at the Huntsman Center in September.
The only other common opponent for the Sun Devils and Cougars was Utah Valley. Arizona State swept UVU 3-0 in Orem and BYU beat the Wolverines 3-1 on Sept. 3, also in Orem.
Defending national champion Texas (23-2) is the No. 1 seed in the tournament, while Penn State got the No. 2 seed, Washington the No. 3 seed and undefeated Missouri the No. 4 seed.
No. 9 San Diego, which outlasted BYU in a five-set thriller to win the West Coast Conference championship, will play host to UC Santa Barbara in the Lincoln Regional.