Injured Mellberg to miss Sweden qualifiers
The Olympiakos centre-back picked up the problem in a friendly against Inter Milan.
"He's not allowed to train for the next two weeks," Hamren told a news conference.
The coach is expected to call up Andreas Granqvist to replace Mellberg in the squad.
Sweden's next qualifier is against Hungary in Budapest on September 2.
"If we win that one, we'll at least make the playoffs," Hamren told reporters.
The nine group winners and the best second-placed team will qualify automatically for next year's finals in Poland and Ukraine, while the eight other runners-up will enter a two-leg play-off for the remaining four berths.
The Swedes, who then travel to San Marino on September 6, are second in qualifying Group E with 15 points from six games.
Their only defeat was by Netherlands, who top the group having won all six of their matches so far.