Lampard suffered the injury during training on Wednesday, and a scan completed earlier today confirmed that he won't recover in time to play this summer.
Liverpool's Jordan Henderson, who was placed on the standby list, is likely to replace Lampard in the 23-man squad should UEFA allow manager Roy Hodgson to make a replacement after the May 29 deadline.
Henderson was a surprise call-up for the standby list two weeks ago, as he has endured a disappointing first season at Liverpool. However, he now finds himself in the squad having played just twice for the national side.
The news comes just days after Gareth Barry was ruled out due to a stomach strain picked up in the friendly with Norway last Saturday.
Arsenal's Jack Wilshere played no part in the season that just finished and was ruled out of the Euros in April. Meanwhile, Michael Carrick was unwilling to be considered as a squad player and wanted guaranteed playing time, so he wasn't chosen.
The injury means that England are starting to lack quality and experience in the centre of midfield. It also puts more pressure on captain Steven Gerrard, who becomes by far the best midfielder on the team.
The news is sad for Lampard, who turns 34 in June, as he is unlikely to get another opportunity to play for his country in another major tournament and could struggle to get back into Roy Hodgson's future plans for the side.