Barkindo, 63, a veteran of the oil industry, was due to step down at the end of this month after six years in the top job at the Organization of the Petroleum Exporting Countries (OPEC).
"We lost our esteemed Dr Muhammad Sanusi Barkindo," NNPC CEO Mele Kyari wrote on Twitter, adding that he died late on Tuesday.
The death is a "great loss to his immediate family, the NNPC, our country Nigeria, the OPEC and the global energy community," Kyari added.
Kyari said Barkindo died hours after meeting Nigerian President Muhammadu Buhari and giving the main speech at an energy summit in Abuja.
His tenure as the head of OPEC has been marked by global shocks that have battered the industry.
During his keynote speech in Abuja hours before his death, Barkindo said the oil and gas industry is "under siege" and still reeling from the enormous investment losses of recent years.
"In a very short timespan, the industry has been hit by two major cycles – the severe market downturn in 2015 and 2016, and the even more far-reaching impact of the COVID-19 pandemic," Barkindo said.
Barkindo's career in the oil industry began in Nigeria in the early 1980s. He served in various capacities at the NNPC and represented Nigeria on OPEC's Economic Commission Board.
He was acting OPEC secretary general in 2006 before returning to the position 10 years later and has led the organisation through a turbulent oil market period including steering it towards greater cooperation with non-OPEC oil producers.
"Serving as Secretary General of OPEC for two terms has been the honour of a lifetime. Over the past six years, we have witnessed both challenging and historic moments, which have underscored time and again the importance of cooperation and teamwork," Barkindo said in his keynote speech on Tuesday.
Diamantino Azevedo, oil minister for OPEC member Angola, told Reuters that Barkindo was always striving to seek consensus for the good of the organisation.
After leaving OPEC, Barkindo was due to join U.S. think tank the Atlantic Council's Global Energy Center as a distinguished fellow, the Council recently announced.
"This tragedy is a shock to the OPEC Family. We express our sorrow and deep gratitude for the over 40 years of selfless service that Mohammad Sanusi Barkindo gave to OPEC. His dedication and leadership will inspire OPEC for many years to come," the OPEC Secretariat said in a Tweet.