Eremenko will be out for at least three weeks, ruling him out of Finland's last European Championship qualifiers against Portugal, team spokesman Lennart Wangel said.
Eremenko, 24, was attacked early Monday after he and his girlfriend left a party thrown by his club, Saturn Ramenskoye, to celebrate the end of the season.
"Two men walked toward them," his father Alexei Eremenko Sr. was quoted as saying by the Finnish newspaper Helsingin Sanomat. "One of them punched him, after which both of them just ran away."
Before the punch, the unknown assailant criticized Saturn and Eremenko for losing Sunday's match against Zenit St. Petersburg, his father told the newspaper.
The win gave Zenit the Russian Premier League title, while a Saturn victory would have made Spartak Moscow champion.
Saturn confirmed the attack and surgery on its Web site, but club officials could not be reached for comment.
Eremenko was already suspended from playing in Finland's Euro 2008 qualifier against Azerbaijan in Helsinki on Saturday. He will now miss the qualifier next Wednesday against Portugal as well, Wangel said.
Finland is fourth in Group A, but has a slim chance of qualifying for next year's tournament if it wins both games.
Eremenko has both Finnish and Russian citizenship.