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, the umbrella body of doctors in the country, says the slow testing process and a lack of adequate protective gear and testing kits are putting medical staff at risk.
President of the association Dr Francis Faduyile told the BBC that it was also important for all patients arriving in hospitals to be tested to determine their coronavirus status before any treatment.
He said this would reduce the risks of medical staff being exposed to the virus.
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”: