Sexton suffered a calf injury during Leinster's 24-24 European Champions Cup draw away to Castres on Friday.
"There's not a lot of damage there, nothing's showing up that's overly significant," said Schmidt.
"We'd be confident he'll be able to train next week and therefore be fully available to face Scotland."
He continued: "Johnny's already starting back doing a little bit."
The New Zealander was also upbeat about the fitness of Sean O'Brien, with the Leinster back-row another player with a calf injury.
"He's slightly further ahead than Johnny," said Schmidt.
"We're confident he may train before the end of the week fully, but he should train fully next week."
Schmidt left out Bordeaux's Ian Madigan from his 40-man tournament squad following the fly-half's decision to play club rugby in France, and brought in Munster's uncapped midfielder Rory Scannell as cover for Sexton.
But he said former Leinster player Madigan could come back into Ireland contention later this Six Nations.
"The first time I saw Rory play for Dolphin against Belvedere he had a fantastic game at 10," said Schmidt.
"There's a big difference between that and Murrayfield but he would be the guy who could cover there.
"We've also got Paddy Jackson available obviously."
He added: "With Ian [Madigan], he could only have done those two first days' training with us. You only get that three-day opportunity with the window. So it complicates that.
"Ian had an injury earlier in the season so he hasn't had a lot of rugby really.
"I've kept in touch with Ian. He would slot back in pretty seamlessly for us, so that's still something potentially that we could look at."
Ireland coach Joe Schmidt expects fly-half Jonathan Sexton to be fit for the Six Nations opener away to Scotland on 4 February.