Branham shares the award with Michigan State's Max Christie.
Branham averaged 18.5 points, 4.0 assists, 1.5 blocks per game and was a combined 15-of-16 from the foul line in a pair of games last week.
Branham is the first Buckeye to earn Big Ten Freshman of the Week honors in back-to-back weeks since DeAngelo Russell won the award in the first two weeks of February in 2015.