Shevchenko, who scored both goals in the 2-1 win over Sweden in their opening match, suffered two blows to his knee in Friday's game against France, Ukraine spokesman Oleksander Hlyvinsky said.
Co-hosts Ukraine lost 2-0 to the French and have to beat England in Donetsk to go through to the last eight.
Hlyvinsky said the injuries sustained by the 35-year-old Shevchenko had generated fluid on the knee.
"Andriy Shevchenko missed training on Sunday due to a knee injury. Shevchenko sustained two painful blows in his knee against France and there is a fluid in his knee that the doctors are trying to pump out," Hlyvinsky told Reuters.
Shevchenko's absence would be a huge setback for Ukraine who have struggled defensively and rely heavily on the attacking instincts of the former AC Milan and Chelsea player.
"Andriy Shevchenko had fluid in [the left] knee joint after the game [against France]. The next day the volume of fluid had increased. This is due to a long-time chronic joint problem. There was a lot of liquid," team doctor Leonid Mironov was quoted as saying by Interfax news agency.
MASSAGE TREATMENT
"We were prepared for this and that is why he was rested from training today. He is receiving massage treatment now. In the evening, all necessary medical procedures will be undertaken. We hope he will be fully fit and ready for the game."
Mironov added that Shevchenko, who has also been dogged by chronic back pain, usually took two to three days to get over such problems.
Coach Oleg Blokhin may give further details on Monday about Shevchenko's chances of being fit for the match.
If Shevchenko cannot play, Blokhin may bring in Serbian-born striker Marco Devic to partner Andriy Voronin in attack.
Shevchenko is Ukraine's record scorer with 48 goals - including his double against the Swedes - 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, but a move to Chelsea proved disappointing. He returned to Dynamo Kiev, where he started his career, in 2009 after a loan spell back at Milan.
Apart from his skill and experience, he is regarded as an inspirational figure whose mere presence on the field can get the best out of his team-mates.
