Smith starred alongside Ricky Tomlinson, Sue Johnson and Ralf Little in the Royle Family.
Little, who played teenager Antony in the show, has led the tributes.
He posted on Twitter: "Devastating to lose two members of my second family in one awful year. RIP Liz Smith. Goodbye Nana. Xxx"
Actor Richard E Grant said: "Liz Smith-I loved working with you on the George Orwell film & privileged to have played & danced together R.I.P."
The episode of the much-loved sitcom in which Nana dies - called The Queen of Sheba - was repeated on the BBC during Christmas week.
In 2009, the Prince of Wales presented Smith, who celebrated her 95th birthday on December 11, with an MBE and told her that the sofa-bound TV characters in the show were "nothing like my family, thank God".
Smith only got her first professional roles in her 50s when Mike Leigh was looking for a middle-aged woman capable of improvisation for his debut feature Bleak Moments.
Her career took off after she played the lead role in his first television film Hard Labour and she once said: "I owe everything to Mike."
The actress played eccentric baker Letitia Cropley in The Vicar Of Dibley but was devastated when her character was killed off, and is now best known for her role as Nana in The Royle Family, for which she won best actress at the British Comedy Awards at the age of 85.
Smith also won a Bafta for Best Supporting Actress for her performance as Maggie Smith's organ-playing mother in the film A Private Function.
