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."

The Games were first held in Hamilton, Canada in 1930, when 11 countries sent a total of 400 athletes to take part.
In Glasgow 2014 there will be more than 4,500 athletes from 71 nations competing in 17 sports over 11 days.
Scotland has previously hosted the event twice, in 1970 and 1986, both in Edinburgh. This will be the first time Glasgow is the host city.
Comments: Will you be watching the Commonwealth Games?
Sporting superstars such as Usain Bolt, Mo Farah and Tom Daley are all competing in what is being billed as the biggest and best Commonwealth Games yet.
The Commonwealth is a collection of countries that are linked in some way to Great Britain, all apart from one - Mozambique.
Many years ago Britain used to control lots of countries as part of something called the British Empire.
Over the years the Empire has disappeared as countries have taken charge of themselves, and has reformed and changed to become the Commonwealth.
All 53 members have signed up to a set of values including democracy, gender equality and international peace and security.
During the opening ceremony the Games will be officially opened by the Queen, who is the head of the Commonwealth.
Africa
Botswana, Cameroon, Ghana, Kenya, Lesotho, Malawi, Mauritius, Mozambique, Namibia, Nigeria, Rwanda, Seychelles, Sierra Leone, South Africa, Swaziland, Tanzania, The Gambia, Uganda, Zambia
Americas
Belize, Bermuda, Canada, Falkland Islands, Guyana, St. Helena
Asia
Bangladesh, Brunei Darussalam, India, Malaysia, Maldives, Pakistan, Singapore, Sri Lanka
Caribbean
Anguilla, Antigua & Barbuda, Bahamas, Barbados, British Virgin Islands, Cayman Islands, Dominica, Grenada, Jamaica, Montserrat, St. Kitts & Nevis, St. Lucia, St. Vincent & The Grenadines, Trinidad & Tobago, Turks & Caicos Islands
Europe
Cyprus, England, Gibraltar, Guernsey, Isle of Man, Jersey, Malta, Northern Ireland, Scotland, Wales
Oceania
Australia, Cook Islands, Kiribati, Nauru, New Zealand, Niue, Norfolk Island, Papua New Guinea, Samoa, Solomon Islands, Tonga, Tuvalu, Vanuatu
List taken from Glasgow 2014 official website
Ireland coach Joe Schmidt expects fly-half Jonathan Sexton to be fit for the Six Nations opener away to Scotland on 4 February.
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The Commonwealth Games take place every four years, with the 2014 event being held in Glasgow, Scotland.