The table-topping Chiefs know they have their home advantage all but secured, but gaining a win over the best Australian side will be a handy confidence boost should they meet again in the playoffs.
McMillan said that while both teams were assured their playoff berths, it was still vital for them.
For the Chiefs, a win would set them up for the backend of the competition, while for the Brumbies, it would give them a chance to claim second place.
"We're playing a team that is extremely hard to play at home. There'll be an element of desperation and what I want to see is that level of desperation matched by us."
The Brumbies have not deviated too far from the traditional forward strength that has characterised their game for many years.
"They've got a strong set piece. Their lineout is a weapon; they've scored more tries [with it] this year than any other team in the competition, not only this year but in previous years, so dealing with that has been a priority with our preparation.
"They've got a good scrum, a hard-working pack and when they carry, they generally get around the corner and have their big blokes quite prepared to run into brick walls. So defensively, we can't allow them to get their game going.
"We're going to have to be disciplined. We can't give them easy piggybacks up the field to feed the game that they want to play."
McMillan said their strength wasn't confined to their pack. They had fast wings that were exciting to watch from afar, and the team was well-drilled.
The Chiefs' choice of Josh Ioane at first five-eighths was a case of getting some game minutes into him.
"He's had a fairly lengthy time out of the game and a couple of runs off the bench, and we're mindful of the fact that if Damian [McKenzie] fell over with Bryn [Gatland] no longer going to see out the season, we have to make sure that we're ticking Josh over.
"And there's also our back three have clocked up a lot of minutes, so Shaun [Stevenson] gets an opportunity to come off the bench this week and freshen up slightly.
"When Laggy [Laghlan McWhannell] is fit and available, he is as good as any lock going around. He's a big lump of a lad, really heavy in his carries; he's physical and, against the Brumbies, that sort of profile will be important to us.
"He's been beavering away the last three or four weeks at club rugby so he's ready and been champing at the bit for his opportunity and with Tupou [Vaa'i] having been left behind to have his All Black rest week it opened the door for us to give Laghlan an opportunity. Hopefully, it takes it with both hands and puts some pressure on us to keep selecting him."