Chief Inspector Olegario Sousa is said to have quit in disgust at the way the missing girl's parents have been treated.
Sky sources said Portuguese police had given their counterparts in the UK 40 questions they want the couple to answer.
Gerry and Kate McCann - who are now back at their home in Rothley in Leicestershire - are expected to be given the list in the next few days.
The couple have been named official suspects in Portugal, and a slew of newspaper reports have linked them to their daughter's disappearance.
They plan to sue one Portuguese paper which said the police believe they killed Madeleine.
Mr Sousa is reportedly upset at leaks to the local press from his officers - leaks which he feels are designed to undermine the couple.
Sky News Crime Correspondent Martin Brunt said: "The official line is that he was taken off the case on Friday because he is the police spokesman, and the case has moved from the police to the prosecution.
"But word on the ground is that some people were unhappy about the leaks to the media.
"His phone was switched off at the weekend, which is unusual because he normally answers it."
Madeleine went missing from her family's holiday apartment in Praia da Luz on May 3.
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