An X-ray showed Elmander sustained a fractured metatarsal in his right foot. He will be examined by Sweden's team doctors before coach Erik Hamren announces his squad in Stockholm on Monday.
Elmander scored twice in the qualifying phase and was almost certain to start when Sweden open their Group D campaign against host nation Ukraine in Kiev on June 11.
The 30-year-old has not given up hope of recovering in time.
"It's hard to give a decision but I hope that it's no worse than that I can come back quickly," he told Swedish television on Sunday.
Sweden also face France and England in Group D.