The announcement comes on the eve of a videoconference by the ministerial monitoring committee of OPEC and its allies in which Novak was due to take part.
"Unfortunately, Alexander Valentinovich Novak has been taken ill with the coronavirus", Prime Minister Mikhail Mishustin told a government meeting in Blagoveshchensk, in Russia's Far East, the Interfax news agency said.
He said Novak learned of the diagnosis after arriving in Blagoveshchensk where he was to take part in the meeting as well as the opening of a huge petro-chemical project near the Chinese border.
"He arrived and he has left for Moscow. With all our hearts, we wish him a recovery," said Mishustin, who himself was diagnosed with the virus in April but has since recovered.
An energy ministry spokesperson said Novak would still participate in Wednesday's videoconference of the so-called OPEC+ group which includes Russia, the RIA Novosti agency said.
It said several journalists accompanying the prime minister on the Far East tour, which began last week, have also tested positive for coronavirus and have been forced to return to Moscow.
Several Russian political figures have been infected with the virus in recent months, including Kremlin spokesman Dmitry Peskov and some ministers and lawmakers.
Russia on Monday had officially recorded 927,745 infections, including 15,740 deaths from COVID-19.
President Vladimir Putin last week said Russia had produced the world's coronavirus vaccine. Officials said on Saturday that the country had produced the first batch of its coronavirus vaccine.