Alexei Kudrin, who is also a deputy prime minister, chairs Alrosa's supervisory board.
"As of this moment, negotiations on Polyus Gold have been suspended because we have failed to agree on terms," Alexei Kudrin told journalists in Cape Town, adding talks were unlikely to be resumed before next year.
He said the disagreements were mainly over the growing price of gold.
"Alrosa is not prepared to accept the terms offered by the sellers," he said.
Polyus Gold is Russia's largest gold producer, accounting for around 20% of Russia's gold output.
Polyus Gold has licenses to gold deposits in Siberia's Krasnoyarsk Territory, Irkutsk Region the Republic of Sakha (Yakutia), and the Magadan Region in the Far East.
Alrosa accounts for 97% of Russian and 25% of global diamond output. It is 37% owned by the Russian government, the Yakutian government owns a 32% stake, the company's employees 23% and the remaining 8% is held by eight districts in Yakutia.
The Russian government is planning to increase its stake in Alrosa to 50% plus one share through an additional issue of shares, planned to be no less than 50% of the current stock, as well as the transfer of former Soviet diamond producer Yakutalmaz's assets to federal ownership.