Dr Lagoo died of cardiac arrest at his Pune residence around 8 pm.
The last rites will be performed after his son comes from the United States, his wife Deepa Lagoo said in a statement.
Dr Lagoo, born in Satara in 1927 and a trained as an ENT surgeon by profession, played an important role in the growth of theatre movement in Maharashtra in post-Independence era alongside Vijay Tendulkar, Vijaya Mehta and Arvind Deshpande.
According to his acclaimed autobiography Lamaan (A porter), theatre bug bit Dr Lagoo when he was in school and he became a part of Progressive Drama Group, a non-commercial group of theatre lovers when he was in B J Medical College, Pune.
Dr Lagoo, however, did not become a commercial actor until he reached his 40s.
He became a surgeon and worked in a hospital in Kenya for some years.
After quitting practise and becoming a full-time actor, he tasted commercial success with V Shantaram's Pinjra (1972).
As an actor, his roles in Marathi plays such as Natsamrat and Himalayachi Saoli, and films like Pinjra made him popular.
In Bollywood, Dr Lagoo essayed memorable roles in films like Ek Din Achanak, Gharonda, Muqaddar Ka Sikandar and Laawaris.
He played Gopal Krishna Gokhale in Richard Attenborough's Gandhi.
Dr Lagoo, affectionately known in theatre circles as 'Doctor', was also known for his progressive and rationalist views.
A Marathi article written by him for the daily Maharashtra Times, captioned 'Parmeshwarala Retire Kara' (It's time to send God into retirement) caused much debate.
He was also instrumental in setting up "Saamajik Krutadnyta Nidhi" (social gratitude fund) for social workers.
Dr Lagoo is survived by his wife, actor Deepa Lagoo, a son and a daughter. His son, Tanveer, died at a young age when a stone hurled by someone hit him while he was travelling by train.
As the news of Dr Lagoo's death spread, condolences poured in from the world of theatre, cinema and politics.
'My tributes to all time great artist Shreeram Lagu. We have lost a versatile personality. A unique theatre actor dominated silver screen and created impact. He was social activist simultaneously,' Information and Broadcasting Minister Prakash Javadekar tweeted.
West Bengal Chief Minister Mamata Banerjee called Dr Lagoo an 'accomplished thespian'.
'Saddened at the passing away of veteran actor Dr Shriram Lagoo. An accomplished thespian, his role portrayals were a hallmark of many Hindi films, Marathi films and stage for over four decades. My condolences to his family and fans,' Banerjee posted on Twitter.
Satish Alekar, a noted playwright, said Indian threatre had lost a giant with the death of Dr Lagoo.
"He was the last soldier who steadfastly believed in freedom of expression and he stood for the freedom of expression during the Emergency," Alekar said.
"He steadfastly stood behind Vijay Tendulkar and other actors of Ghanshiram Kotwal and Sakharam Binder."
Rishi Kapoor remembered Dr Lagoo as one of the most spontaneous actors.
'R I P. One of the most natural spontaneous actors, Dr. Shreeram Lagoo sahab leaves us. Did several films way back. Unfortunately never got to work with him in the past 25/30 years. He had a retired life in Pune. Love you Dr. Sahab,' Kapoor tweeted.
NCP chief Sharad Pawar described Lagoo as a doyen of experimental theatre who had intellectual awareness and exercised a great influence on the world or arts.
"Both young and veteran artistes found could rely on him from support. Death of this great actor is a big loss," Pawar said.
Film-maker Madhur Bhandarkar said: 'Saddened to hear demise of veteran actor Dr. #ShriramLagoo sir. He was great socialist and versatile actor, his contributions will always be remembered for his memorable roles in theatre & films. #OmShanti.'
'With a very heavy heart, our nation bids adieu to the legend rightly considered as one of pioneers of the Indian theatre, Dr. Shriram Lagoo. The man of many faces, his eternal legacy will continue reign the hearts of millions! Rest in peace, Natasamrat,' Bharatiya Janata Party leader and former Maharashtra minister Vinod Tawde said.
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