The documents, almost 50 pages in all, were found in a soggy heap behind a bus stop in Kent early on Tuesday morning.
One set of documents discusses the likely Russian reaction to the ship's passage through Ukrainian waters off the Crimea coast on Wednesday. Another details plans for a possible UK military presence in Afghanistan after the US-led Nato operation there ends.
A member of the public, who wishes to remain anonymous, contacted the BBC when he realised the sensitive nature of the contents. The BBC believes the documents, which include emails and PowerPoint presentations, originated in the office of a senior official at the Ministry of Defence (MoD).
The government said an investigation had been launched.
A Ministry of Defence spokesperson said an employee had reported the loss of sensitive defence papers, adding: "It would be inappropriate to comment further."
As we reported earlier, Russian naval aircraft opened fire on a British ship in the Black Sea.
The Russian side claimed that HMS Defender entered Russia's territorial waters near cape Fiolent in the Black Sea. According to them, the incident took place at 11.52 a.m. Wednesday. The British crew was warned about the weapon use in case of the border violation, but they did not respond.