Michael Adebolajo, 32, claimed five prison officers assaulted him at London's high-security Belmarsh prison two years ago, but they were cleared of blame.
The UK Ministry of Justice (MoJ) said it would "robustly defend" the claim.
"The public will be rightly outraged at the thought of this man receiving compensation from the taxpayer and we robustly defend claims made against the Prison Service," an MoJ spokesperson said.
'The Sun' newspaper first reported the story of the compensation claim, the value of which remains unknown.
UK judicial guidelines suggest awards for the loss of two front teeth are between 3,000 and 5,500 pounds but figures can increase depending on the extent of the injury and treatment needed.
Adebolajo lost his teeth while he was being held at Belmarsh on remand after the killing near Woolwich barracks, and claimed he had been assaulted by the prison officers.
The Prison Officers' Association insisted only approved techniques had been used in restraining Adebalajo.
Muslim converts Adebolajo and Michael Adebowale are serving life for killing Fusilier Rigbyin May 2013.
