Dundee have taken four points from two Clydesdale Bank Premier League games since Brown took over on an interim basis, with the gap at the bottom now cut to 14 points following Wednesday's 2-1 victory over St Mirren.
Inverness travel to Dens Park on Saturday looking to consolidate their top three place against a team they have twice beaten 4-1 this season but Butcher knows they will face a stern test.
Butcher said: "John Brown has certainly fired his team up well, he is a real motivator.
"I have known him for a long while. I played against him when he was at Dundee and played with him at Rangers.
"He's a great leader and a great character too.
"You wouldn't want to get on the wrong side of John, that's for sure.
"But he is certainly inspiring his team to fight and scrap and play some decent football, and they have had some decent results so far.
"We certainly expect to play a team that's well up for the game and we're looking to trying to get another three points."