Kilbane, 32, is set to make his 100th appearance for the Republic of Ireland in Wednesday's World Cup qualifier against Montenegro.
Brown told the Tigers` official website: "It's fantastic for Kevin and it's certainly good for ourselves to be involved with an international of such stature.
"Kevin brings a certain calmness to the table when he plays his football and that is why he is still involved at international level. He came to the football club as a wide-left player - he has played centre midfield for us, forward, left-back and centre-back.
"That shows the versatility of the lad but it's the mentality and the invaluable experience that he brings to us and his country that is the reason he's still playing great football."
Former Everton, Sunderland and West Brom player Kilbane joined Hull from Wigan in January.