Grosso underwent medical tests near the team's base in Florence on Tuesday. The Italian Football Federation said he had returned to his club Inter Milan and would not begin training again until next week.
Attacking left-back Grosso, a member of Italy's World Cup-winning squad, will also miss the Group B game in Georgia on Oct. 11.
Italy coach Roberto Donadoni has not called up a replacement for Grosso and his most likely solution against Ukraine in Rome is to ask Gianluca Zambrotta to switch to the left side of defence.
The world champions have made a poor start to Euro 2008 qualifying with a 1-1 draw at home to Lithuania and a 3-1 defeat in France.
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