He reportedly died on Wednesday afternoon at Avenues Clinic in Harare where he was being treated.
Efforts to obtain comment from his wife Daisy and daughter Selmor were fruitless as they did not take calls or respond to messages.
However, politicians, musicians and fans were already sending condolence messages on social media.
“Rest in peace Oliver Mtukudzi. If anyone ever made me proud to be Zimbabwean, it was you. Thank you for making us happy for so long, especially during the darkest days,” said former education and sports minister David Coltart on Twitter.
The news of Tuku’s death comes after he lost his son Sam – a successful musician in his own right – in a car accident in March 2010.
Tuku was born into a family of six. One of his sisters and his only brother are also deceased.
Member of parliament for Norton constituency Temba Mliswa confirmed the untimely departure of the music great.
Mliswa said he would petition President Emmerson Mnanagwa to accord national hero status to Mtukudzi.
“I have it on good authority that Dr Oliver Mtukudzi is no more. We’ve lost an icon and my heartfelt condolences to Daisy and family. I’m writing to the president to apply for National Hero status for his contribution to the music, arts and culture industry,” he said.
Scores of fellow artists said the music industry had been robbed.
Former prominent disc jockey Eric Knight said: “I’m devastated to let you know that the Mountain has fallen.”
Tuku boasted a string of hit albums such as Bvuma (Tolerance), Vhunze Moto, Tsivo (Revenge), Dairai (Believe) among others.
His notable hit songs included Neria, Svoyi Yangu (My Love), Patapata, Izere Mhepo (Full of Bad Omen), Perekedza Mwana (Escort the Girl), Tozeza Baba (Afraid of an Abusive Father) among others.
Apart from being a musician, Tuku was a businessman, philanthropist, human rights activist and UNICEF goodwill ambassador for southern Africa.
He is considered to be Zimbabwe’s most renowned and internationally recognised cultural icon.