Agent Barry Langford, who confirmed the news, said she had a "zest for life and was a fantastic actress".
Mr Langford said Tamm had been saddened by the recent deaths of contemporaries Elisabeth Sladen, who played Sarah Jane Smith in Doctor Who, and Angharad Rees, who died last weekend.
"She was a darling companion and wonderfully witty and kind," said Tom Baker, who played the fourth Doctor. "I'm so sorry to hear of her death."
Mary Tamm is best remembered for her role as fellow Time Lord Romanadvortrelunder or Romana (Fred for short), when she made her debut in the Series 11 (1978/9) story 'The Ribos Operation, the first story in the 'Key To Time' series story arc.
Actress Helen Lederer, a friend of Tamm's, said: "Mary was such an energised, talented woman with a great twinkle in her eye and she was so very beautiful."
Tamm was born in Bradford, West Yorkshire, the daughter of Estonian refugees, and had a long career on stage and screen.
Tamm leaves behind husband Marcus Ringrose, daughter Lauren and seven-year-old grandson Max.