Randle, a freshman forward from Dallas, averaged 16.5 points and 14 rebounds in UK's wins over LSU and Ole Miss.
Against LSU, Randle was held to eight points, but pulled down a game-high 15 rebounds and scored the game-winning basket with 3.9 seconds remaining in overtime.
Randle is just six double-doubles shy of tying DeMarcus Cousins and Anthony Davis for the most by a UK freshman. Dan Issel holds the program record with 25 in one season.
It marked the second SEC Player of the Week honor for Randle's career. He has also earned SEC Freshman of the Week honors. That honor went to Vanderbilt's Damian Jones this week, who averaged 16.5 points and 5.5 rebounds against Missouri and Auburn.
Kentucky returns to action on Thursday, Feb. 27, at Rupp Arena against Arkansas. Tipoff is slated for 7 p.m. ET on ESPN.