The data related to soldiers from the Military Reaction Force (MRF), an elite unit which is alleged to have shot unarmed civilians in Northern Ireland during the Troubles in the early 1970s, according to the Independent.
The information was reportedly among separate material downloaded from an online cache on to a memory stick and handed by an inexperienced Panorama researcher to a third party, in protest at the way the BBC programme was handling a documentary about politics in the London Borough of Tower Hamlets.
The material was believed initially only to relate to people who had contributed to a Panorama piece investigating alleged questionable practices in the borough, and was passed on to the office of the mayor of Tower Hamlets, Lutfur Rahman.
But the Independent claimed it also contained confidential and sensitive information relating to a previous Panorama programme, Britain's Secret Terror Force, broadcast in November.
The identity of at least one MRF serviceman is said to have been compromised, while the file also contained names and details of other senior military figures.
The newspaper said the Panorama security lapse came during the making of the Tower Hamlets documentary when BBC application forms for covert filming in Northern Ireland were duplicated for use as a basis for applications to film undercover in London.
Sensitive details in the originals were not deleted, but the copy of the file given to Tower Hamlets has now reportedly been destroyed.
The Information Commissioner's Office is investigating the data breach, the Independent said, which could lead to a criminal prosecution.
An ICO spokesman told the newspaper: "We will be making inquiries into the circumstances of the alleged breach of the Data Protection Act before deciding what action, if any, needs to be taken."
A BBC spokesman said: "There has been a lot of baseless speculation on the circumstances surrounding this programme. It's not appropriate for us to comment further while there is an investigation by the ICO under way."