The video, which was shot at Khan's Bandra home, will not be aired and the footage is to be kept for family viewing, according to Mid Day.
The 3 Idiots star said: "Half the time I shot the campaign, Azad was in my lap. Once when [my wife] Kiran wasn't around, we even shot a promo featuring Azad.
"At first, I told her that we shot a promo with him and it looked very good. Then I told her that I was kidding and we wouldn't use it."
Khan and his wife Kiran Rao announced the birth of their son Azad Rao Khan on December 1 through a surrogate mother.
The actor described his five-month old son as a happy baby with a good temperament. However, he explained that due to work commitments he only sees Azad at night.
"Earlier, I was working from home, so I spent a lot more time with him. But now that I'm shooting and return late, I wake him up very gently," he said.
"When he sees me, his face lights up. I spend an hour or so with him before going to bed."
Khan described his new TV show as an emotional rollercoaster ride, adding: "One thing that is anchoring my emotions while the show is on is the presence of Kiran and Azad around me."