"I feel on good form. Nothing is bothering me now," the former AC Milan and Chelsea forward said, apparently referring to a thigh injury and an old back problem.
"My fitness is good. I hope to improve it even further during training," the national information centre Ukraine-2012 quoted him as saying on its website.
"I will do my best to be on top form for the Euros," the 35-year-old added.
Ukraine, who are co-hosting the June 8 to July 1 tournament with Poland, have only uncapped goalkeepers in the squad and a weak defence.
They are drawn in Group D with Sweden, France and England.
Shevchenko is the all-time top scorer for Ukraine with 46 goals and was European Footballer of the Year in 2004.
He scored 175 goals for Milan between 1999 and 2006, winning a Champions League final in 2003, though a later spell at Chelsea proved disappointing.
Some commentators say just Shevchenko's presence on the pitch would be an inspiration for the Ukrainian side and he is included in the 26-squad named by manager Oleg Blokhin.
But it is not clear if he will make an appearance on the field.
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