The festival will be held from April 21-26 at The ArcLight in Hollywood.
The salute to Kapoor will include screenings of his classic films Lamhe and Virasat as well as the world premiere of the English language version of Gandhi, My Father, which he produced.
Kapoor first appeared on the big screen in Hamhare Tumhare in 1979 and his first lead role followed four years later in Who 7 Din.
'With the incredible success of Slumdog Millionaire, the timing could not be better,' Kapoor said. 'I feel as though I have come full circle. In November, I attended the AFI Fest premiere of Slumdog Millionaire at the ArcLight Theatre.
'Now, some five months later, I am humbled and honoured that my work as an actor and film-maker has been chosen to receive such a fantastic tribute at the same venue.'
Yes Madam, Sir profiles Dr Kiran Bedi, the first woman to join the Indian Police Service and a controversial and inspiring figure in India.