With 11 minutes remaining in the game and the Buckeyes leading 50-45, Sylvester hit Furman's Nick Sanders with a flagrant elbow to the head while lined up for a free throw.
"What Matt did last night is unacceptable and he needs to learn this lesson," O'Brien said. "Yes, emotions run high and frustration sets in during the heat of games but he needs to know how to control his emotions and that what he did was wrong."
As part of Sylvester's suspension, he will issue a written apology to Sanders, O'Brien said.
Sylvester will not travel to New Jersey this weekend for Ohio State's game against Seton Hall at noon Saturday (ESPN Plus/WBNS 10 TV).
The Buckeyes (5-3) return to Columbus for a Dec. 23 game against Eastern Illinois at Value City Arena (8 p.m./ESPN Plus/WBNS 10 TV).