Drogba, 31, was knocked out in a collision with Canaries' goalkeeper John Ruddy and was carried off on a stretcher wearing what appeared to be a breathing aid after receiving seven minutes' treatment at Stamford Bridge.
The Ivorian was taken to hospital from the game but was later released, with Chelsea confirming on their official website that the club's medical staff would need to "continue to monitor" the Ivorian in the coming days.
Chelsea and Norwich were locked at 1-1 when Drogba left the pitch but after Ruddy was later sent off for a tackle on Ramires, Villas-Boas' side went on to win the game.
"We are just waiting for the full exams on his concussion and hopefully nothing is wrong,'' Villas-Boas said. "He is showing some good signs of recovery for us to be a little bit more tranquil.''
Villas-Boas had no problem with Ruddy's challenge but said of the incident: "It looked pretty nasty. He lost consciousness completely on the pitch.
"I have to be very, very grateful, not only to my players but to the Norwich players and to my medical staff for reacting so quickly to a potentially dangerous situation.''