It is understood Michael Adebolajo, of Romford, east London, lost two front teeth in Wednesday’s alleged attack.
No arrests have been made.
The Old Bailey trial of Mr. Adebolajo, 28, and co-accused, Michael Adebowale, 22, from Greenwich, south-east London, has been set for 18 November.
Mr. Adebolajo is also accused of the attempted murder of two police officers and possession of a firearm with intent to cause others to believe that violence would be used.
A Prison Service spokesperson said: “The police are investigating an incident that took place at HMP Belmarsh on 17 July.
“It would be inappropriate to comment while the investigation was ongoing.”
Prime Minister David Cameron joined thousands of mourners at Fusilier Rigby’s military funeral at Bury Parish Church in Greater Manchester on Friday.
The 25-year-old soldier’s commanding officer, Lt Col Jim Taylor, said in a eulogy he was “larger than life [and] was always at the centre of fun and mischief, but he was a true regimental character with real charisma and everybody fell under his spell”.
After the service, his body was driven along roads lined by mourners for a private burial at Middleton Cemetery.