McCarthy, who has been almost ever-present under O'Neill, has now returned to training after missing Ireland's warm-up games against Netherlands and Belarus.
"It's hamstring, groin injuries. I should be fine (for Sweden)," he told British media.
"I am back training and delighted to be back with the squad.
Hopefully now I can kick on and step up the fitness."
Ireland have been drawn in Euro 2016 Group E with Sweden, Italy and Belgium.
"We have got a tough group," said McCarthy. "Each and every one of us who is going on the plane and travelling to France, we know it's going to be tough but there's a real excitement about the place."
(Reporting by Nivedita Shankar in Bengaluru; Editing by Tony Jimenez)
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