Brown will make it four centuries of Celtic appearances if he plays in Wednesday’s Ladbrokes Premiership encounter with St Johnstone, which could see the champions go 22 points clear at the top.
The 31-year-old is in his 10th season at Celtic Park and quickly won over Rodgers when the former Liverpool boss took charge last summer.
Rodgers said: “It’s a remarkable achievement by a top-class professional.
“I didn’t know that’s what it was but to play that number of games at a club this size, your professionalism, your enthusiasm, your energy for the game and your commitment to being a top professional has to be there.
“I’ve said it on many occasions since I walked in the door here and my general first impressions on him have been very, very positive.
“And he’s a remarkable leader. I have to say, working with him on a day to day basis, the players in the changing room take a great lead from him.
“He’s at the very front from the very first steps we make on the training field, the warm-up, right from the very, very start he sets an incredible example.
“He shows a great example to the other players and he is playing at the top of his game this season. So 400 would be great for him but I think there is quite a few more to come as well.”