The investigation was launched after the FBI referred the matter to the Pentagon on Sunday.
FBI agents last night called to the home of the woman whose affair with retired General David Petraeus led to his resignation as CIA director on Friday.
A spokeswoman for the FBI says that agents went to Paula Broadwell's home in Charlotte, North Carolina.
FBI spokeswoman Shelley Lynch declined to say what the agents were doing there.
FBI agents appeared at Ms Broadwell's home carrying the kinds of cardboard boxes often used for evidence-gathering during a search.
A senior US defence official said Gen Allen's communications were with Ms Kelley, who has been described as an unpaid social liaison at MacDill Air Force Base, Florida, which is headquarters to the US Central Command.
Kelley is said to have received threatening emails from Broadwell, who is Petraeus' biographer and who had an extramarital affair with Petraeus that reportedly began after he became CIA director in September 2011.
Allen, a four-star Marine general, succeeded Petraeus as the top American commander in Afghanistan in July 2011.
The senior official said Panetta believed it was prudent to launch a Pentagon investigation, although the official would not explain the nature of Allen's problematic communications.
"Gen Allen disputes that he has engaged in any wrongdoing in this matter," the official said.
Panetta said that while the matter is being investigated by the Defense Department Inspector General, Allen will remain in his post as commander of the International Security Assistance Force, based in Kabul.