Coach Erik Hamren also picked goalkeeper Andreas Isaksson, who has been suffering from a shoulder problem.
As Tuesday's UEFA deadline passed for the registration of 23-man squads for next month's tournament in Ukraine and Poland, Galatasaray forward Elmander underwent an X-ray in Gothenburg to assess the state of his injury.
"The healing is going as it should," team doctor Leif Swardh told reporters following the X-ray.
"I increasingly hope that he will be ready to play the first game at the Euros."
Sweden play co-hosts Ukraine in their opening Group D fixture in Kiev on June 11 before taking on England and France.
The final Swedish squad shows no changes from that originally announced by Hamren on May 14.
Hamren has chosen not to risk John Guidetti, who had a sensational season on loan at Feyenoord from Manchester City.
The young forward, who netted 20 goals for the Rotterdam club, has not yet made a full recovery from a virus.
Goalkeeper Isaksson, who kept goal in nine of Sweden's 10 qualifying games, has declared himself fit after being sidelined by a shoulder injury since early March.
"Now it feels a lot better, I think it's good now," he told reporters after a training session on the island of Gotland on Sunday.
Goalkeepers: Par Hansson (Helsingborgs), Andreas Isaksson (PSV Eindhoven), Johan Wiland (Copenhagen).
Defenders: Mikael Antonsson (Bologna), Andreas Granqvist (Genoa), Mikael Lustig (Celtic), Olof Mellberg (Olympiakos), Jonas Olsson (West Bromwich Albion), Martin Olsson (Blackburn Rovers), Behrang Safari (Anderlecht).
Midfielders: Emir Bajrami (Twente Enschede), Rasmus Elm (AZ Alkmaar), Samuel Holmen (Istanbul BB), Kim Kallstrom (Olympique Lyon), Sebastian Larsson (Sunderland), Anders Svensson (Elfsborg), Pontus Wernbloom (CSKA Moscow), Christian Wilhelmsson (Al Hilal).
Forwards: Johan Elmander (Galatasaray), Tobias Hysen (IFK Gothenburg), Zlatan Ibrahimovic (AC Milan), Markus Rosenberg (Werder Bremen), Ola Toivonen (PSV Eindhoven). (Editing by Mark Meadows)
