The bodies of a man and a woman, both believed to be aged between 40 and 50, were recovered from Breydon Water, Great Yarmouth, Norfolk Police said.
The force said the deaths were currently unexplained.
Search teams were called to the area shortly after 11:20 BST when a member of the public reported seeing the bodies on a mudbank.
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Police were joined in their search by the coastguard and Norfolk Fire and Rescue Service.
Det Insp Chris Burgess of Norfolk Police, who is overseeing the inquiry, said: "We're unsure if it is a crime."
He said he did not know how long the bodies had been in the water or on the mud.
Asked whether the bodies may be those of missing people known to the police, he said: "Not that we've identified at this stage, no."
In a further statement, Det Insp Burgess said: "It has taken some time for officers to recover the bodies due to where they were discovered.
"The deaths are currently being treated as unexplained. We are in the early stages of the inquiry and it would be inappropriate to speculate any further."
Post-mortem examinations would be held in due course to establish the cause of death, police added.
Breydon Water is a large expanse that opens into the sea through the port of Great Yarmouth.
The rivers Yare, Waveney and Bure flow into Breydon, which connects the northern Broads to the southern Broads.
The area is tidal and currents can be significant. High water on Thursday morning was at 08:38 BST.
Two bodies have been recovered from water after they were spotted on a tidal mudbank in Norfolk.