Dr Mackinnon was involved with the organisation and wider peace moment in Scotland for 30 years.
A member of the Communist Party of Great Britain, he co-ordinated protests against the Gulf War, and challenged the American response to 9/11.
The GP had undergone treatment for cancer and had been diagnosed with a terminal illness.
The Scottish CND said Dr McKinnon had "constantly strived" to build opposition to Trident and had made a "detailed case" that more jobs could be sustained in Scotland by diverting money spent on nuclear weapons into other projects.
In a post on the Scottish CND website, a spokesman said: "He showed a determination to make a positive contribution to the world, despite his own health problems. This was shown when, after retiring as a GP and undergoing treatment for cancer, he went to Sierra Leone to work for Medecins San Frontieres.
"In recent months, disabled and confronting a terminal illness, he persisted in helping with Scottish CND street stalls throughout the general election.
"Alan's dedication to peace and nuclear disarmament has been an inspiration to us all and his loss will be greatly missed."
Dr Mackinnon is survived by his wife Karin and his children, Maeve and Ian.
Former chairman of the Scottish CND and anti-war campaigner Alan Mackinnon has died after an illness.