Jeremiah Adebolajo told the BBC that he speaks to his brother almost daily, and had also spoken to his lawyer and to the governor of Belmarsh Prison, where the incident is said to have occurred.
Five members of prison staff have been suspended after the 28-year-old suspect was injured on Wednesday at the prison in south-east London.
The Prison Officers' Association (POA) said he was being restrained using approved techniques, and that its members strenuously denied any wrongdoing.
Adebolajo told the BBC his brother said five officers at a time are present when dealing with him and he is never in contact with any other prisoner.
He said the altercation began when his brother was given an instruction by one of the guards.
He said: "They decided to twist his arm back... the arm that had been shot... He manoeuvred out of that so they smashed his head against a window."
Adebolajo added: "I wonder why it took five prison officers to restrain one man and how in the course of that restraint his teeth were able to be knocked out if they were following procedures.
"The suggestion is that procedures means that prisoners' teeth are going to be knocked out."
POA chairman Peter McParlin accused the Ministry of Justice (MoJ) of over-reacting to the situation.
He told BBC Radio 4's Today programme: "We have spoken to our members and on the basis of what our members have told us they have done absolutely nothing wrong.
"We are concerned that the Ministry of Justice have over-reacted due to the notoriety of this prisoner."
McParlin criticised the MoJ for failing to "correct false reporting" of the incident at Belmarsh.
He said that while restraint techniques were designed to minimise injuries to staff and prisoners, "sometimes there are unforeseen consequences in any violent incident".
A POA official said earlier this week that it will fully co-operate with any police investigation, and expects the officers to be "fully exonerated".
A Metropolitan Police spokesman said: "We can confirm that an allegation of assault was passed to the Metropolitan Police Service on July 17 by Belmarsh prison. An investigation has been started."
Adebolajo is accused together with Michael Adebowale, 22, of hacking Fusilier Rigby to death near Woolwich Barracks in south-east London on May 22. The pair are due to stand trial at the Old Bailey on November 18.