Nyan Win had been a member of the National League for Democracy's Central Executive Committee as well as a confidante of Suu Kyi.
Suu Kyi and top members of her party and government, including Nyan Win, were arrested when the military seized power in February. The military-installed government has since arrested thousands of mostly young people who protested its takeover.
The death of Nyan Win, 79, came as Myanmar is reeling from soaring numbers of COVID-19 cases and deaths that are badly straining the country's medical infrastructure, already weakened when many state medical workers went on strike to protest the army's seizure of power.
Charity workers and cemetery staff say hundreds of people in Yangon, the country's biggest city, are dying daily due to suspected cases of COVID-19, particularly from a lack of medical oxygen to help them breathe.
The country's overcrowded prisons are especially susceptible to the spread of the virus, according to the Assistance Association for Political Prisoners, which has done surveys of detention facilities.
Deputy Information Minister Zaw Min Tun said Tuesday that 375 people have been confirmed to have COVID-19 in prisons across the country, the Voice on Myanmar online news service reported.
Many believe the real number is much higher. Neighboring Thailand has recorded more than 39,000 COVID-19 cases in its prison population since the beginning of April.
Health authorities on Tuesday reported 5,860 new COVID-19 cases, bringing Myanmar''s official total since the pandemic began to 240,570. There were 286 new deaths recorded, bringing the total to 5,567.
Nyan Win, who was charged with sedition, had been confined in Yangon's Insein Prison, which for decades has held many prominent political prisoners. Suu Kyi is being held under house arrest at an undisclosed location in the capital, Naypyitaw.
He was moved from Insein Prison to Yangon General Hospital's intensive care unit on July 11 after testing positive for the virus. It is believed he had underlying health problems.
Nyan Win's death was confirmed by his lawyer, San Mar La Nyunt, who said she reached him in a video call Tuesday morning, just minutes before he died.
Lawyers for some inmates at Insein Prison told US government-funded broadcaster Radio Free Asia on Friday that there are about 50 confirmed COVID-19 cases there. The prison began a two-week lockdown on July 8 due to the virus surge.
Detained American journalist Danny Fenster, also held in Insein Prison, told his lawyer last week he believes he has COVID-19, but prison authorities deny he is infected. Fenster, managing editor of Frontier Myanmar, an independent online news outlet based in Yangon, has been charged with incitement for allegedly spreading false or inflammatory information.