Azarov bet Swedish fan Ola Sjostedt a beer that Ukraine would beat Sweden in their opening Group D match in the tournament last Monday.
When the home team beat the Swedes 2-1, Azarov duly invited Sjostedt to sup a beer with him at government offices in Kiev.
A widely-distributed photograph showed the usually-dour white-haired prime minister smiling broadly, a Ukrainian football scarf round his neck, as he raised a pint of beer with his Swedish guest.
With political infighting in Ukraine running at a high pitch, the opposition was quick to pounce.
Leading opposition deputy Mykola Tomenko, in a statement on an opposition party website, reminded the 64-year-old Azarov that drinking alcohol - even weak alcohol - was strictly prohibited on official premises.
"It is shameful and inadmissible when the leaders of the country contradict the law and the principles of defending morality by beginning to publicise consumption of strong drink during working hours and on state premises," said Tomenko.
He said Azarov should pay a fine of 85 hryvnias ($10) - the usual level of punishment for an administrative offence - and he called on the Kiev police to take necessary action to see this was done.
