"The police are investigating an incident that took place at HMP Belmarsh on 17 July," said a Prison Service spokesman.
"It would be inappropriate to comment while the investigation was ongoing."
Adebolajo and co-accused, Michael Adebowale, 22, are due to face trial in November over the horrific knife attack that claimed the life of Fusilier Lee Rigby in Woolwich on May 22.
Rigby was hacked to death in broad daylight before Adebolajo delivered an Islamist tirade to passers-by.
British Prime Minister David Cameron joined thousands of mourners last week at the soldier's funeral.
Cameron gathered with some 800 of Rigby's family members and colleagues for the private military funeral at a church in Bury, near Manchester in northwest England.
Thousands of members of the public lined the surrounding streets.
The killing stunned Britain and sparked a rise in community tensions. Several mosques have been attacked while the far-right British National Party and English Defence league have held a string of anti-Islamic rallies.