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.
“Frank Lampard experienced his highest high when he finally lifted the Champions League trophy as Chelsea beat Bayern Munich in the Allianz Arena on 19 May.
“Now he faces the grim reality that his England career at the highest level is over.”
“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.
“You can’t compare Jordan Henderson to Frank Lampard and that’s not being disrespectful to Jordan Henderson.
“Frank Lampard, with a wealth of experience, made his debut against Belgium 13 years ago.
“Jordan Henderson has only made two appearances and you cannot compare the two. It’s a devastating blow for Lampard and England.”
“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.”
Manager Roy Hodgson is already without another experienced midfielder in Barry, who was ruled out of the tournament after suffering a groin injury in the 1-0 win over Norway.
If Henderson, 21, is allowed to replace Lampard then Liverpool will be the most represented club in Hodgson’s squad, with five, despite a disappointing season which saw them eighth in the Premier League.