He also asked them to upload the pictures on 'Narendra Modi App' or 'MyGov' to give the occasion a new dimension.
"Grandparents, parents and children should together perform yoga and also upload their photos. It will be such a pleasant blend of yesterday, today and tomorrow -- lending a new dimension to yoga," PM Modi said in his 'Mann ki Baat' radio address.
"These pictures will be a guarantee of a brighter tomorrow."
PM Modi expressed his gratitude to the person who sent him this suggestion.
"I feel that as our 'Selfie with Daughter' campaign proved to be a very inspiring experience, this campaign of posting pictures of three generations performing yoga together will evoke curiosity across the nation as well as the world."
PM Modi urged people to spread awareness about the coming yoga event.
"We are still left with about three weeks for the International Yoga Day. Start practicing from today itself. From June 1, I will post something or the other about yoga on Twitter and continue to do so till June 21. I will share with you. You too kindly spread the message of yoga and connect people with it," he said.
The Prime Minister said this, in a way, is a movement for preventive healthcare.
He invited people to connect with the occasion, saying "in a very short time, the festival got worldwide recognition as the World Yoga Day and is connecting people."
"At a time when separatist forces are raising their ugly heads, this has been India's great contribution to the world. We have successfully connected the whole world through yoga. Like yoga connects the body, mind, heart, and soul, similarly it is connecting the world now."
"Because of lifestyle, because of a mad race to achieve success, and because of increasing responsibilities, leading a stress-free life has become very difficult... this situation is coming up even at a comparatively younger age. Yoga is a guarantee of wellness and fitness both. Yoga is not merely an exercise," he said.
PM Modi said that he sent letters to all governments and all world leaders about the Yoga Day two days ago.
Remembering his last year's announcements on yoga competitions and awards, he said: "we shall gradually advance in that direction."