Alisher Usmanov, the second largest shareholder in the English Premier League team Arsenal, stumped up the cash after a request from the Russian government, according to Russian media reports.
Sports Minister Vitaly Mutko asked him to give the Russian Football Union (RFS) a subsidized loan worth €5.24 million to cover part of the wages in a bid to "save Russia embarrassment", especially as it prepares to host the World Cup in 2018.
Capello and the team’s general manager, Oreste Cinquini, are reportedly owed around €7.9 million and were last paid in June, the month Russia was booted out of the World Cup in the group stage.
The RFS said in November it could no longer afford to pay the wages.
Mutko said on Thursday that the salary issues would be resolved within the next couple of days.
"We spoke with Alisher Usmanov for around an hour and managed to get things sorted out,” he told the news agency RBC-Sport.
"As a citizen of Russia, he would also have been embarrassed that we as a country that plans to host the next World Cup cannot even pay the head coach of Russia."
Capello’s salary was estimated at €9 million when he took the job on, making him the highest-paid coach at last summer's World Cup in Brazil, according to a Forbes ranking.
But following Russia’s early exit from the tournament, Capello was described as a "thief" by a far-right politician and summoned to the Russian parliament to explain himself.