The party raised concerns over what it called a “totally unwarranted and indeed unconstitutional political intervention” after reports that senior civil servants had suggested the Labour leader was “too frail” to be prime minister.
In a letter, Jon Trickett, the shadow cabinet office minister, told Sir Mark Sedwill, the cabinet secretary, that the allegations were “disturbing”.
The row followed claims, reported by The Times, that senior civil servants attending a recent event had raised concerns about Mr Corbyn’s fitness.
One reportedly said: “There is a real worry that the Labour leader isn’t up to the job physically or mentally but is being propped up by those around him. There’s growing concern that he’s too frail and is losing his memory. He’s not in charge of his own party.”
Another is quoted as saying: “When does someone say [he] is too ill to carry on as leader of the Labour Party, let alone prime minister? There must be senior people in the party who know that he is not functioning on all cylinders.”
Mr Corbyn hit back within hours, dismissing the story as “a farrago of nonsense” and insisting he was a “very fit, very healthy, very active person”.
In his letter, Mr Trickett said the claims about Mr Corbyn’s ill-health were “manifestly untrue”.
He wrote: “Discussion of these matters, based on false assumptions, should not be taking place. Worse, it is without precedent in my experience that any high-level discussion about senior politicians, let alone the leader of the opposition, should be shared with a newspaper.
“I must now formally say to you that it is hard to avoid the conclusion that this has been a totally unwarranted and indeed unconstitutional political intervention with disturbing implications for our democratic system.
“There clearly needs to be an investigation into what appears to have been a breach of civil service neutrality, independent of the Cabinet Office, in order to avoid any real or apparent conflicts of interest.”
Mr Trickett also requested a meeting with Sir Mark to discuss the “deeply concerning development” and asked for assurances “that the basic principles of British public life will not be undermined”.
Rumours about Mr Corbyn’s health have been swirling around Westminster for several months.
Labour has strongly denied suggestions that its leader suffered a minor stroke earlier this year, and that he is sometimes taken home during the day for “afternoon naps”.
It has insisted he frequently cycles and runs for between five and seven kilometres several times a week, although admitted he is receiving treatment at Moorfields Eye Hospital in London for a muscle weakness in his right eye.