Leeds-born Kay, who was best-known for writing TV hits including Fat Friends, Band of Gold and The Syndicate, died on Sunday, her production company has said.
A spokesperson from Rollem Productions said: "It is with profound sadness that we announce the untimely and sudden passing of our beloved friend, mentor and colleague Kay Mellor on Sunday, May 15.
"We have lost a phenomenal talent and a true luminary. We ask that you please respect the privacy of the family and friends at this time."
Kay began her career writing for Coronation Street and Brookside in the 1980s and went on to create the BBC's Playing the Field.
She is also known for writing Fat Friends starring Ruth Jones and James Corden and The Syndicate in 2012.
In 2010, she was made an OBE, and in 2014 she was handed the Outstanding Contribution to Writing award at the Writers' Guild Awards and was made a fellow of the Royal Television Society.
Kay and her husband Anthony were married in 1968 and have two daughters, actress Gaynor Faye and television producer Yvonne Francas.
Tributes from stage and screen have been made to Kay.
Former Emmerdale actress Hayley Tamaddon tweeted: "Such sad sad news about the wonderful Kay Mellor.
"She was always so lovely and kind to me... a truly brilliant lady."
Emmerdale's Danny Miller also tweeted his sympathies.
He said: "Devastated to hear of the passing of Dear Kay Mellor. An incredible talent in the TV world and someone who always had a warming smile on offer with open arms.
"Sending all of my love to Gaynor and the rest of the beautiful family during this difficult time"
The BBC's chief content officer, Charlotte Moore, said: "I'm shocked and deeply saddened to hear that Kay Mellor has suddenly passed away.
"Kay was an outstanding writer and the creative force behind many of the nation's best-loved television dramas.
"She wrote with such heart, humanity, humour and passion with strong female characters often taking centre stage.
"She will be missed and our thoughts are with her friends and family at this difficult time."
Leeds Civic Trust said: "Kay Mellor, a true friend of the Trust and a champion of Leeds and the North. Thank you for your incredible contribution to our city. We send our deepest sympathies and condolences to the family."