The actor, who was born in The Gambia and lived in Hampstead, London, was a long-standing anti-racist activist and campaigned for racial equality within the acting profession.
He was one of the first Black actors to join the Royal Shakespeare Company in the 1960s.
His agency confirmed news of his death in a statement on Twitter.
It said: “It is with great sadness that we announce the passing of our wonderful client, Louis Mahoney.
“Louis paved the way for many actors who followed: a lifelong activist and champion of antiracism.
“His warmth and good humour will be sorely missed. A celebration of his life will follow.”
Louis worked as part of the Equity actors union to improve the representation of BAME actors on British television.
The union said: “We are saddened to learn of the death of former Vice President Louis Mahoney.
“Louis was a passionate activist on behalf of @EquityUK and led the union’s fight against racism and apartheid for many years.”
Writer and producer Jack Thorne was one of the first to pay tribute, saying: “Louis Mahoney was one of those actors who could carry a whole world through his eyes.
“Perhaps because he led such an extraordinary life.
“Worked with him on @kibwetavares’s film Jonah (where he played Daniel Kaluuya’s older self) and he was so magnificent.”
Emmerdale actor Bhasker Patel recalled the help Louis had offered him, saying: “Always enjoyed #LouisMahoney’s guidance when needed from day one entering our ACTING profession.
“Thank you for your tremendous work and knowledge supporting all of us.”
A post on The Royal Court’s Twitter account said: “We’re so sad to hear of the passing of Louis Mahoney.
“A brilliant actor and the most wonderful human being; a devoted activist and extraordinary performer, he will be sorely missed.
“Here we remember him in our 2011 production of debbie tucker green’s truth and reconciliation.”
The Bridge Theatre and actor Vas Blackwood, who has appeared in The Lenny Henry Show and Casualty, was also among those paying tribute.
Louis played the doctor in the 1975 Fawlty Towers episode The Germans, which recently re-entered the news after it was temporarily removed from the UKTV streaming platform.
The famous “don’t mention the war” episode was initially removed because it contained “racial slurs”, according to UKTV.
Louis also appeared in a string of Doctor Who episodes and TV shows including Runaway Bay, Harbour Lights and Oscar Charlie. This year he featured in BBC One’s The Split.