The managing director of Nigerian National Petroleum Corporation Limited Mele Kyari said Barkindo died about 11pm on Tuesday (8am Sydney time).
Cause of death was not made public.
His death came just hours after a meeting with Nigerian president President Muhammadu Buhari who had described the Barkindo, as a "worthy ambassador of the country" commending him for his service to OPEC.
Barkindo served as secretary general from 2016. Prior to that he served as acting secretary general and represented Nigeria on OPEC's Economic Commission Board during 1993-2008.
"Certainly a great loss to his immediate family, the NNPC, our country Nigeria, the OGPEC and the global energy community," Kyari said.
"Burial arrangements will be announced shortly."
Barkindo completed a BA in political science from Ahmadu Bello University in Nigeria, in 1981 and Master of Business Administration at Washington University in 1991. Prior to MBA, in 1988 he earned a postgraduate diploma in Petroleum Economics from Oxford.
Just a day ago, Barkindo spoke at a conferencde warning the oil and gas sector was "under siege" and now facing "huge challenges on multiple fronts."
He said the ongoing war in Ukraine, the pandemic, inflationary pressures, underinvestment and a potential recession were to blame.
"These threaten our investment potential now and in the long term, to put it bluntly, my dear friends, the oil and gas industry is under siege," Barkindo said.