Russell sustained the injury in Glasgow Warriors' Pro12 semi-final defeat by Connacht in May.
"We don't expect him to play in the first two or three games of the season," Townsend told BBC Scotland.
"We'll just see what happens over the next few weeks."
Russell was stretchered off during Glasgow's defeat in Galway after a sickening collision with team-mate Zander Fagerson in the first minute of the match.
The Scotland playmaker was kept in hospital for over a week for observation, but is now back in light training.
"He's working on skills, he's very keen to be involved," Townsend continued.
"Everything has gone well so far with his recovery, but obviously we're being very cautious on when he can come back to training with the team and also full training.
"So far his progress has been really good."
Glasgow Warriors head coach Gregor Townsend says Finn Russell is progressing well in his recovery from a serious head injury, but still expects him to miss the start of the season.