The Saracens flanker was a disappointing performer as the Scots opened their RBS 6 Nations campaign with a heavy 28-6 loss to Ireland in Dublin last Sunday.
His place in the side has gone to Glasgow's Chris Fusaro, while vice-captain Greig Laidlaw will now lead the side out against the Auld Enemy when they visit Murrayfield for the evening kick-off.
Brown's omission is one of three changes to the starting XV following the Aviva Stadium loss, with centre Matt Scott replacing the benched Duncan Taylor and Glasgow wing Tommy Seymour coming in for injured club-mate Sean Maitland, who has been ruled out the rest of the Championships with knee and ankle injuries.
Fusaro's call-up is his first for the senior squad and the 24-year-old said: "I'm absolutely delighted. Being the Calcutta Cup, there's no better game to get your first cap. I'm still pinching myself a bit."
On the bench, Glasgow's Jonny Gray replaces his British and Irish Lion brother Richie - who like Brown does not make the matchday squad at all - while experienced hooker Scott Lawson has been given the nod over Pat MacArthur.
Johnson said it had been a "difficult" decision to omit Brown but that Fusaro's skills as a ball-winner on the deck had been key in the selectors' deliberations.
"Fusaro is picked to do a certain role and we believe there's an opportunity for him to do it," said the Australian.
"England are powerful, they have an edge to their side and are assertive and aggressive. They will probably consider themselves unlucky last weekend but it's not always brute force that wins these games."
Of the other changes to the starting team, Johnson added: "I spoke to Tommy Seymour in the summer that he needed a point of difference. One of the things that comes to mind is his aerial skills. He possesses natural aerial skills from his time in Ireland. Every time he has gone up in class his skills have transcended."
Johnson said that Duncan Taylor's form made it a tough decision for him to begin on the bench rather than the starting XV but the Saracens' man's ability to cover a number of positions in the backline had been a factor, especially in the aftermath to the injury to Maitland.
Johnson also is excited by the resumption of the centre partnership between Scott and Alex Dunbar which shaped very promisingly during last summer's tour to South Africa.
He added: "We are all looking forward hugely to Saturday's match. You want the rivalry that exists. It's intense and great to be part of."