The Hoops captain reached 300 appearances for the club at Dundee United yesterday afternoon.
Brown joined the Bhoys in 2007 and hasn't looked back since, with many of his 300 games for the club coming as captain.
And Mulgrew, who stood in for Brown as skipper while he was out injured earlier this season, has heaped praise on the 29-year-old, stating that 'a player of his quality' deserves to play so many matches for the SPL champions.
“Scott has done really well since he arrived at Celtic. A lot of those 300 appearances have been as captain as well, which is a big achievement," Mulgrew told Celtic's official website.
“You can understand why a player of his quality has played this many games for Celtic.
“I’m sure there’s plenty more to come from Scott and I can only wish him all the best for the future.”
The Hoops lost 2-1 at Dundee United yesterday afternoon but remain four points above them, still top of the league table.