Emeka Chugbo was taken to Lagos University Teaching Hospital on Monday with “severe symptoms” and died on Wednesday, according to the hospital.
The 60-year-old doctor also had a history of asthma, his friend Lawal Oyeneyin told local media.
The patient at Dr Chugbo’s clinic who had Covid-19, the respiratory disease caused by the virus, died last week.
On Saturday a medic in northern Nigeria, Aliyu Yakubu, became the first doctor to die of coronavirus in the country.
The Nigerian Medical Association (NMA) has in the past urged the state governments to provide enough protective gear to all health workers.
The association urged patients to be honest about their medical, travel and contact history to help doctors quickly identify a potential coronavirus case.
Friends and family have been paying tribute to Dr Chigbo.
He “exhibited exemplary brilliance and showed empathy for his patients”, former colleague Dr Oyeneyin told reporters.
“RIP Unc!,” tweeted a loved one who also called the late doctor “one of the smartest people I ever knew”: