Eggs from peregrine falcon nests at three different sites in the Peak District were taken in early spring, Derbyshire Police has revealed.
The force said there could be a number of individuals or groups responsible as part of a "black market trade".
Derbyshire Wildlife Trust said the eggs may have been removed while volunteers - who patrol the White Peak area - were forced into lockdown in late March.
Rural crime officer PC Karl Webster said the eggs would be worth a lot.
"We believe they're taking them to hatch," he said.
"There's a lucrative Middle Eastern falconry market allied to this country, an investigation two to three years ago confirmed that."
The birds of prey, which were heavily persecuted in the 1960s and suffered from the impact of pesticides, have recovered in numbers in recent years.
However, they are still illegally killed and targeted for their eggs and chicks, according to the RSPB.
David Savage, from Derbyshire Wildlife Trust, said the taking of eggs was "sickening".
"We began the season with great hopes and tried to keep an eye on them as much as we could, but unfortunately when we couldn't watch them 24 hours a day, they were taken," he said.
"It has been difficult to monitor the site in lockdown - the end of March and early April was when our volunteers were indoors."
In May, the RSPB said it had been "overrun" by reports of birds of prey being illegally killed since the lockdown across the UK.