Brown had been a doubt with an ankle injury he picked up in Saturday's 2-0 win over Macedonia.
"Scott's fine," said Burley. "He jarred his ankle - did not actually get a knock. He's going to be training on Tuesday afternoon."
Burley revealed he would assess the fitness of goalkeeper Craig Gordon, who has been nursing a thigh strain.
He added: "He played on Saturday, came through fine, had a reaction and we will assess his fitness on Wednesday morning.
"If Craig was fit it would be a big bonus for us. We'll just have to wait and see."
One player who will definitely be missing for Scotland is James McFadden, who scored the second goal against Macedonia.
The Birmingham man is suspended for the Hampden Park clash after he received a yellow card at the weekend, but Darren Fletcher believes there is enough quality to replace him.
The Manchester United midfielder said: "James is a great player and a top scorer. He is a bit of an enigma really for Scotland. But it gives someone else an opportunity to come in. Even though James is a massive miss, we have good quality to come in and replace him."
Burley reckons Wednesday's game will be one of the biggest of his managerial career.
"I think so," he said. "From a player's points of view, from a manager's point of view, it doesn't come any bigger."