The Steppenwolf canceled Monday's scheduled performance in honor of Mahoney.
Born in Blackpool, Lancashire, England, on June 20, 1940, Mahoney moved to the US after visiting his sister who married a USA serviceman during World War II.
Mahoney was also a member of Steppenwolf theatre company for 39 years, and the company announced his death on their social media accounts.
Kelsey Grammer's Frasier and David Hyde Pierce's Niles, both psychiatrists with lofty views of their own intellect, squabbled constantly with their dad but, when needed, the family closed ranks. He served in the United States army for three years, which he credited with eradicating his native British accent.
Born on June 20, 1940 in Bispham, England, Mahoney started his career with theatre in 1977 and joined films three years later. "We were all blessed to have spent 11 glorious years together", Greenberg wrote alongside a picture of the show's cast with Mahoney. Though some stage actors scoff at sitcoms, Mahoney told Time Out, "Frasier was a classy gig".
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Mahoney died of cancer Sunday in Chicago.
Peri Gilpin, who played Roz Doyle in Frasier, shared a photo of Mahoney singing at her wedding - praising his good humour and urging fans to "remember him well".
Director Greg Berlanti tweeted that Mahoney had been "so kind and supportive of me early in my career", helping to get the film The Broken Hearts Club made.
According to the Steppenwolf website, Mahoney's theater appearences included The Herd, The Seafarer, The Rembrandt and I Never Sang for My Father ( Steppenwolf ); The Outgoing Tide, A Life ( Northlight Theatre ); Prelude to a Kiss ( Broadway ) and Romance ( Almeida Theatre ), among others.