The former Chelsea player was ruled out of Ukraine's penultimate training session before they face England in Donetsk because of a knee problem.
A Ukraine football association spokesman said: "Andriy suffered a kick to his knee during the second half against Sweden and then another kick in the same area against France. He is unable to train today and I would say he is doubtful for Tuesday."
He went on: "He has seen the doctor and is now having treatment. We hope he can still take part but I repeat, he is doubtful."
If Shevchenko is ruled out, it will be a massive blow to his side's hopes of reaching the quarter-finals of the European Championship for the first time.
The 35-year-old Dynamo Kiev striker may be at the veteran stage of his career but scored both goals in his side's 2-1 win over Sweden.
Shevchenko has also featured in all four previous meetings with England, stretching back to May 2000.
England are currently second in Group D, level on four points with leaders France, while tournament co-hosts Ukraine have three points.