Hamrén said that he had been assured by team doctor Leif Swärd that the 30-year-old former Toulouse and Bolton Wanderers player would be fit in time for their opening Group D match against co-hosts Ukraine on June 11.
Elmander, who has been capped 63 times, scoring 16 goals, broke the bone during his side Galatasaray's 0-0 draw at rivals Fenerbahce on Saturday that saw them take the Turkish title.
"For me, Johan is an integral element in our team and I am going to take a gamble following the advice of Leif," said Hamrén.
The 20-year-old striker, who has been viewed as the natural successor to Ibrahimovic, has not played for his Dutch club Feyenoord since April 14th because of a nervous affliction that sees him lose all feeling in his right leg from time to time.
However, Hamrén did also include experienced attacking midfielder Sebastian Larsson, who underwent a hernia operation on April 24th.
The Swedes play all their matches in Kiev, following up their clash with Ukraine with games against England on June 15th and France on June 19th.
The Scandinavian side have two warm-up games prior to leaving for the tournament on June 6th -- against Iceland in Gothenburg on May 30th and Serbia in Stockholm on June 5th.