The 30-year-old former Toulouse and Bolton striker suffered the injury on May 12th and hopes to be fit for Monday's opening Group D match against Euro 2012 co-hosts Ukraine although no decision was expected before Saturday at the earliest.
The former Bolton player's progress means that Sweden's coach will have almost a full squad to choose from for Monday's game, with only central defender Daniel Majstorovic ruled out with a long-term injury.
Despite being at full strength, Hamrén has played down Sweden's chances, in their Euro opener, pointing to Ukraine's home advantage.
"They've got the support of the home country. That's the reason why they're obviously favourites," for the Group D opener on Monday in Kiev, Hamrén said to journalists this week after the team arrived at their Kiev base.
Sweden will also play France and England in the group, with the Scandinavians coming into the tournament on a high after a 3-2 friendly win against Iceland and a 2-1 victory over Serbia.