Lampard, who has won 90 caps since making his international debut in 1999, pulled his thigh in training on Wednesday and was examined by the England medical staff following a scan.
England have already lost Gareth Barry to injury this week and fellow midfielder Scott Parker has only just returned to action after struggling with an Achilles problem.
"It's a huge blow for the team, especially coming after the loss of another senior player in Gareth Barry," England manager Roy Hodgson said on the FA website.
"The fact that the doctor cannot guarantee Frank could take part in any of the group matches means we have to replace him in the central midfield area."
"Apart from it being a huge blow to me and the team, I'm especially disappointed for Frank himself. He has been in very good form and was looking forward to the tournament.
HUGE CONTRIBUTION
"He made a huge contribution towards us qualifying for the Euros so it is cruel to be forced out through injury just before the tournament."
The FA said Liverpool midfielder Jordan Henderson, capped twice, will be called into the squad subject to agreement from UEFA's medical team.
Everton's Phil Jagielka replaced Barry in the squad on Monday after the Manchester City midfielder tore a muscle in his lower abdomen during Saturday's 1-0 friendly win over Norway in Oslo.
England play Belgium in a friendly at Wembley on Saturday and open their Euro 2012 campaign against France in Donetsk on June 11. Sweden and co-hosts Ukraine are also in Group D.
Chelsea's Lampard was not certain to start against France given that Liverpool midfielder Steven Gerrard was handed the captain's armband by Hodgson.
While Lampard and Gerrard are key men for their clubs, they have never flourished as a partnership in central midfield for England.
