"Berezutsky won't be able to regain his form in time for the tournament," Advocaat told reporters following the opening day of Russia's training camp.
Berezutsky, who along with his twin brother Alexei played at Euro 2008, where Russia reached the semi-finals, has been out since hurting his hip last month.
"Unfortunately, the injury turned out to be worse than was first diagnosed," said the CSKA Moscow central defender.
"I still feel discomfort when I try to run and I don't want to jeopardise my team by going to the Euros unprepared."
Advocaat said Sporting midfielder Marat Izmailov, who this month earned a surprise recall to the national team, would be dropped from a preliminary 26-man squad if he did not report to the training camp by Monday.
"If he is not here by tomorrow than he should just stay in Portugal," said the Dutchman, who will step down as Russia boss following the tournament to take charge of Dutch club PSV Eindhoven.
Izmailov, due to play for Sporting in Sunday's Portuguese Cup final, was not sure he could make the deadline.
"I have some other team commitments after the cup final," the 29-year-old, who has not played for Russia since 2006, was quoted as saying by local media last week.
Euro 2012, co-hosted by Poland and Ukraine, starts on June 8 when Russia play the Czech Republic, while Poland face 2004 European champions Greece in the other Group A match.