A prominent filmmaker said that he was "disgusted" by the scene, Mid Day reports.
"We grew up watching Doordarshan. That tune is sacred. To ridicule it shows a lack of sensitivity," he said.
A veteran television actor said: "I love Farhan and Zoya's cinema and they come from a distinguished film family. Why should they satirise a revered institution?"
Farhan Akhtar, who plays a lead role in the film, defended the scene, saying: "That scene was not an after-thought. It was part of the script. We grew up at a time when that tune was integral to our lives. When we'd be out playing cricket, we could hear the Doordarshan tune from our windows and it signalled the end of our game.
"In the same way, it signals the end of the holidays for the three characters in Zindagi Na Milegi Dobara. I wish people would look beyond Hrithik's humming and understand why it was done."
Akhtar added of co-star Roshan: "The way his character loosens up in the film is a mirror of what happened to Hrithik as an actor. He has realised he doesn't have to be in the rat race. He agreed to play a role that isn't the central one in this film - it was very generous of him."
Zindagi Na Milegi Dobara has become the biggest Hindi film of 2011 in the overseas market.
> Read our Hrithik Roshan Zindagi Na Milegi Dobara interview here
Watch the trailer for Zindagi Na Milegi Dobara below: