The Ministry of Defence (MOD) said the employee concerned with the loss of documents reported it last week, and the department has launched an investigation.
A member of the public, who wanted to remain anonymous, contacted the BBC when they found 50 pages of classified information in a soggy heap behind the bus stop early on Tuesday morning.
According to the BBC, the papers contained a set of documents that discuss potential Russian reaction to HMS Defender's travel through Ukrainian waters off the Crimea coast on Wednesday.
Other documents outlined plans for a potential UK military presence in Afghanistan.
An MOD spokesperson said: "The Ministry of Defence was informed last week of an incident in which sensitive defence papers were recovered by a member of the public.
"The department takes the security of information extremely seriously and an investigation has been launched.
"The employee concerned reported the loss at the time.
"It would be inappropriate to comment further."
Shadow defence secretary John Healey called the incident "as embarrassing as it is worrying for ministers".
"It's vital the internal inquiry launched by the Secretary of State establishes immediately how highly classified documents were taken out of the Ministry of Defence in the first place and then left in this manner," he said.
"Ultimately, ministers must be able to confirm to the public that national security has not been undermined, that no military or security operations have been affected and that the appropriate procedures are in place to ensure nothing like this happens again."
Cover image: The MOD main building (Picture: PA).