De Rossi was taken off early in the second half of Monday's 2-0 win over Spain and team doctor Enrico Castellacci said on Wednesday that he had taken a severe knock.
"He is working very hard, we are doing everything for him to recover and we can't give a time frame but we are aware that the problem is serious," he said.
Midfielder Antonio Candreva's groin strain has also not recovered enough for him to return, the team doctor said.
"Candreva has tried to recover in every possible way, working very hard," said Castellacci. "There has been a significant improvement but not enough for him to be reintroduced into the team."
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De Rossi's absence would be a blow for coach Antonio Conte with Thiago Motta, his most likely replacement, also missing through suspension.
Veteran De Rossi was used sparingly in the qualifiers but he has been back in favour during the tournament, proving himself to be an important figure for Italy.
(Writing by Brian Homewood in Paris. Editing by Adrian Warner.)
