Griner is the first Baylor player to win the award. She received 36 votes Saturday from the 40-member national media panel that selects the weekly Top 25.
The 6-foot-8 post averages 23.4 points, 9.4 rebounds and 5.2 blocks on the season and shoots 61.1 percent from the field and 80.4 percent from the free throw line.
Griner out-paced Elena Delle Donne of Delaware who received two votes, while Notre Dame's Skylar Diggins and Stanford's Nnemkadi Ogwumike received the other votes.
Griner's win ended a run of three straight seasons that a Connecticut player has been player of the year, Maya Moore won the award last season.
Earlier, Griner was named a WBCA All-American and has also received All-American status from the USBWA and the Wooden Award.
Mulkey has guided her team to an undefeated season, and Baylor needs two more wins to become the first team in NCAA history to win 40 games in a season.
She was presented the award after receiving 19 votes from the 40-member national media panel. Baylor has topped the AP poll for the entire season and claimed both the Big 12 Conference's regular-season and postseason crowns.
The Lady Bears are appearing in their second Women's Final Four in the past three seasons.