Cech was forced off at half-time of the third-round tie at Stamford Bridge after suffering a head injury in a collision with Orlando Sa.
Villas-Boas revealed Cech had been given the all clear.
"Petr went for a scan in the hospital and he's okay," he said.
"He felt a little bit dizzy from the early concussion at half-time.
"We decided, and he decided as well, it was better not to take risks."