The Scotland skipper returns to the Hoops side for Wednesday night's Champions League meeting with Barcelona at the Nou Camp following a three-match European ban.
The jury is still out whether or not Brown belongs at this level of competition and Mjallby suggests this is the perfect stage for him to set the record straight.
"He hasn't got a point to prove to us, he is one of our best players, he is very important and we have missed him a lot," Mjallby said.
"But maybe for himself and the public, he can prove that he can play at this level."
He added: "The target is to finish off this campaign on a good note.
"We are disappointed that we don't have a chance of European football in the new year but it is a hard group and there is not much we can do now.
"It is a good chance to take on more experience at this level."
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