The news was confirmed after the Chelsea midfielder, 33, was examined by medical staff after a scan.
Liverpool midfielder Jordan Henderson will be called into the squad, subject to agreement from Uefa's medical team.
"It's a huge blow for the team, especially coming after the loss of another senior player in Gareth Barry," said manager Roy Hodgson.
"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 added."He has been in very good form and was looking forward to the tournament. 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."
Chelsea's Lampard is one of the most experienced players Hodgson had to call upon, with 90 caps.
BBC Sport's chief football writer Phil McNulty believes Lampard's absence will be a big loss to the squad.
"Frank Lampard has occasionally been a maligned figure for England - but his loss from the Euro 2012 squad will be a heavy blow for manager Roy Hodgson," he said.
"Lampard has maturity, experience and continues to be a winner as proved by his vital role in Chelsea's Champions League and FA Cup victories.
"He may not have started England's first Euro 2012 game against France but his presence and professionalism around the squad is always beneficial and he would have been determined to force his way into the side.