The Galatasary forward fractured a metatarsal as his side won the title against Fenerbache and it was feared that he would miss the tournament.
"The injury he has is the best one can get, if one has a fractured foot. He can walk on it already," Hamren told a media conference in Stockholm.
The Swedes open their campaign against Ukraine in Kiev on June 11 and are in the same group as England and France.
There was no place for John Guidetti who had a stellar season on loan at Feyernoord from Manchester City. The raw teenager scored 20 goals for the Rotterdam club as they secured second place in the Dutch league.
But a virus meant that he missed Feyernoord's run-in and opened the door for Marcus Rosenberg of Werder Bremen.
The Swedes will be led by AC Milan forward Zlatan Ibrahimovic but the defence will have to cope without Celtic centre-back Daniel Majstorovic, who has ruptured knee ligaments.