He passed away at 5.15am in Mumbai.
Kapoor had been staying at the Breach Candy Hospital for the past month, suffering chronic renal failure.
Saira Banu, Shammi Kapoor's co-star in Junglee, told NDTV that the loss was "Unbelievable. We keep talking to each other, keep meeting at functions. He comes in a wheelchair. Went to Pran's birthday last year."
The actress recalled her last meeting with Kapoor: "When we were to meet at Aamir Khan's nephew's marriage, this was the last time we met. Don't have words. He (Shammi Kapoor) used to drive his own car even after dialysis. So fond of driving his own car. I can't believe this, how did this happen? He was perfectly well.
"Never imagined this could happen to him. Just don't associate that this could happen to a man who was so bubbly. When he was sick, he didn't look like he wanted sympathy. Will be remembered, [he is] irreplaceable. Can't say more, too shocked."
Born Shamsher Raj Kapoor on 21 October, 1931, Kapoor was the middle son of theatre and film actor Prithviraj Kapoor and the younger brother of showman Raj Kapoor.
Kapoor debuted in Bollywood in 1953 with Jeevan Jyoti and went on to deliver hits such as Dil Deke Dekho, Junglee, Professor, China Town, Kashmir Ki Kali, Teesri Manzil, An Evening in Paris, Bramhachari and Vidhaata.
Kapoor was associated with the swinging '60s, and a large part of his appeal stemmed from his exuberant performances of songs such as 'O haseena zulfon wali' and 'Aaja aaja main hoon pyar tera'.
Shammi Kapoor was due to play the shehnai in Imtiaz Ali's Rockstar alongside grand-nephew Ranbir Kapoor.
"In my younger days, I used to play the shehnai or would enact it to perfection. I think I can do it today, also," he said.
"As a child, Ranbir would sit on my lap and sing classical music to me. He wasn't trained in that but did it just to bug me."
Amitabh Bachchan said on Twitter: "Shammi Kapoor ji passed away this morning at 5.15am... Rushing there now... the flamboyance and joie de vivre of the Industry lost!
"An entire life full of optimism and happy spirit, caring loving to all... Now suddenly silent."
The funeral for the Bollywood legend will be held on August 15 at 11am at Banganga crematorium, Mumbai.