Brown was crowned player of the tournament at the 2014 Six Nations and is a nominee for another individual accolade, having been included on a six-man shortlist for the Aviva Premiership Player of the Year award.
His "phenomenal" performances will probably not be enough to guide Quins to the Premiership final on May 31, so Brown should be in England's team for the first Test against the All Blacks a week later.
Care believes that this is the perfect stage for Brown, 28, to show that he is up there with the best players in his position as he goes head-to-head with New Zealand number 15 Israel Dagg.
He told reporters: "Mike's had a phenomenal season. He'll clean up at our Quins awards and I'd be shocked if he isn't right up there to win this. He's had a brilliant season and I don't think he's had a bad game all year. That's what you need - consistency of performance. He's not just done it for Quins - he's done it for England too, as we've seen during the Six Nations.
"Mike has never been shy of confidence and he's a very competitive person who doesn't want to give anyone else a shot at the 15 shirt. That's the way you have to be. He's very professional, looks after himself a lot and lets his rugby do the talking.
"Mike's right up there at the moment. On current form he's one of the best, if not the best, full-backs in the world. Israel Dagg is a wonderful player and I'm sure Mike will be looking forward to testing himself against him in his own backyard."
Brown scored four tries in his five appearances at this year's Six Nations.