Scotland Yard stressed that the document, sent on Friday, was a routine part of their inquiry but would not reveal what the letter said.
The communications have been used to ask the Portuguese police to carry out certain pieces of work on the British force's behalf.
Deputy Assistant Commissioner Martin Hewitt said that so far no requests to carry out interviews or arrests had been made. He said: "This is part of an ongoing process. The way this investigation is working at the moment is we are using that process, letters of request, and they are now going to be going out routinely."
Detective Chief Inspector Andy Redwood has travelled to Portugal again this week for a routine meeting with investigators there.
Madeleine, who was then nearly four, disappeared from her family's holiday apartment in Praia da Luz in the Algarve on May 3 2007.