Burden had been considered questionable after getting injured against Georgia in the second quarter last week.
Drinkwitz told ESPN that Burden took part in Missouri's "Fast Friday" practice and walked through on Thursday after missing practice the prior two days.
"He looked great," Drinkwitz said of Burden after Friday's practice. "He's going to play."
Burden is one of the country's top wide receivers, amid a breakout season that has him ranked second in the SEC in receptions (64) and third in receiving yards (958).
He is both Missouri's top receiver and the program's best player, and his presence is critical for the No. 14 Tigers to keep up with the No. 13 Volunteers.