The 35-year-old centre has already played his final match for Ireland and enjoyed an emotional send off at the Aviva Stadium.
But with Leinster looking to advance in Europe, Madigan insists the club's fortunes will take priority over O'Driscoll's long goodbye.
"I think he writes his own script," Madigan told the Irish Times.
"He's the consummate professional. Everything that comes his way he deserves. Going down to Toulon next week, we can't be emotionally attached to that. It was the same going to France in the Six Nations. You can't be thinking about that.
"What we have over them is that we're playing for the club we grew up in.
"You're representing your club, where you grew up and where you come from. I would like to think that's going to give us the edge next week.
"I think when the going gets tough, away from home, when your backs are against the wall and you've got a best friend either side of you, it's going to definitely make a difference."