MacLennan, founder of the internationally renowned A Play, A Pie and A Pint, in Glasgow, was described as a giant of theatre.
Susannah Armitage, producer of A Play, A Pie and A Pint, said: "Everyone at Oran Mor is devastated today by the loss of our friend and colleague David MacLennan. He was a passionate, kind and intelligent man who launched the careers of many and whose presence in the building will be sorely missed.
"We will continue to produce A Play, A Pie and A Pint in his memory. Personally, he was my great friend and mentor and I will miss him terribly."
Oran Mor, formerly Kelvinside Parish Church, is Gaelic for "great melody of life" or "big song", symbolic of the sweep of its intent.
The producer was co-founder of stage companies 7:84 and Wildcat, which lasted for two decades.
His personality and reputation allowed him to draw major talent in the form of Robbie Coltrane, Bill Paterson and Elaine C Smith to his theatre in the west end.
Laura Mackenzie Stuart, port-folio manager for theatre at Creative Scotland, said: "Today, we learn about the loss of a true giant of theatre in Scotland. David MacLennan's influence cannot be overstated, from pioneering work with companies such as 7:84 and Wildcat through to his revolutionary A Play, A Pie and A Pint at Oran Mor, David has been instrumental in helping to shape the world-class theatre we have in Scotland today.
"He was much loved, but he leaves behind an impressive legacy for us to learn from and build on."
Playwright Alan Bissett wrote on Twitter: "David MacLennan has died. Titanic figure at the heart of Scottish theatre. A dreadful loss. Much love to his family."
The writer Stephen Greenhorn, said: "Scottish Theatre, its writers especially, owe a great deal to David MacLennan. A huge influence, now sorely missed.
Playwright and theatre director David Greig said: "David MacLennan shaped Scottish theatre and touched the lives of nearly everyone in our business."
Theatre company Paines Plough also wrote on Twitter: "RIP David MacLennan, legendary founder of Play, Pie, Pint. A genius producer and a great man," while Tam Dean Burn, the actor, said: "Thoughts go out to all of David MacLennan's family and friends. A very sad day."
Actor Colin McCredie said: "The saddest news ever. Can't believe we've lost this giant of Scottish Theatre."
MacLennan, who was married to actress and Balamory star Juliet Cadzow, was the son of two Glasgow doctors. His sister, Elizabeth, and her playwright husband John McGrath, were also co-founding members of the 7:84 theatre company, which pioneered some of the most radical political drama seen in Scotland and the UK.
A spokeswoman for the Citizens Theatre said: "Greatly saddened to hear of the passing of David MacLennan, a hugely inspirational figure in Scottish theatre.
"He will be missed by all."
Laurie Sansom, artistic director of the National Theatre of Scotland, which is producing the The Great Yes, No, Don't Know Five Minute Theatre Show this summer, which was co-curated and will feature writing by MacLennan, said: "We all knew the was unwell, but of course it is still a shock.
"I got to know him when I first moved here 15 months ago and he was such an enthusiastic supporter of theatre in Scotland and the community of Scottish theatre workers.
"What he achieved with Play, Pie and a Pint was without precedent, and was an extraordinary achievement."
Culture secretary Fiona Hyslop said: "David MacLennan was an incredibly talented writer, actor and producer whose work has been an inspiration to many, bringing insight, passion and pleasure to audiences across Scotland and around the world. My condolences go to his family and friends."