Ekdal fell over a table in a nightclub at the beginning of May, opening a cut in his back that required stitches and an overnight stay in hospital.
Sweden coach Erik Hamren told reporters on Tuesday that he may not be fit to start in their opening Group E fixture against Ireland, but he might yet play some part.
"Albin has made great progress during the week and it feels good," Hamren said. "He is not a player that will start against Ireland, but he could be a very good player to finish the game against Ireland."
Niggling injuries and the late arrival of some players from their clubs mean Sweden's preparations for the finals are only just beginning, Hamren said.
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"We have been together for a week but we haven't trained with the whole group yet," he noted. "The more time we have together, the more we can practise things."
Sweden, who will also face Italy and Belgium in Group E, will meet Wales in Stockholm on Sunday in their final warm-up game before the tournament starts.
Squad
Goalkeepers: Andreas Isaksson (Kasimpasa), Robin Olsen (Copenhagen), Patrik Carlgren (AIK Stockholm)
Defenders: Ludwig Augustinsson (Copenhagen), Mikael Lustig (Celtic), Andreas Granqvist (Krasnodar), Erik Johansson (Copenhagen), Victor Nilsson Lindelof (Benfica), Martin Olsson (Norwich City), Pontus Jansson (Torino)
Midfielders: Jimmy Durmaz (Olympiakos Piraeus), Albin Ekdal (Hamburg SV), Emil Forsberg (Red Bull Leipzig), Oscar Hiljemark (Palermo), Kim Kallstrom (Grasshoppers), Sebastian Larsson (Sunderland), Oscar Lewicki (Malmo), Pontus Wernbloom (CSKA Moscow), Erkan Zengin (Trabzonspor)
Forwards: Marcus Berg (Panathinaikos), John Guidetti (Celta Vigo), Emir Kujovic (IFK Norrkoping), Zlatan Ibrahimovic (Paris St Germain)
(Compiled by Philip O'Connor; Edited by Ken Ferris)
