Lee will also miss Florida State's Nov. 10 trip to No. 11 Virginia Tech.
Lee began the season behind Weatherford, but replaced him during Florida State's 21-14 win over Alabama. He started the Seminoles' next three games, but after Lee's seven turnovers contributed to back-to-back losses at Wake Forest and against Miami, Weatherford was put back into the starting lineup last Saturday against Duke.
Lee, a junior from Daytona, Fla., completed 53 percent of his passes, throwing five touchdowns and running for three more in the four games he has appeared in.