A copy of the order, seen by Reuters, instructs police not to release any information about the results of investigations, police raids or other operations before July 25.
The World Cup, which Russia is hosting for the first time, ends on July 15 and the Kremlin is keen to use the tournament, which opened on Thursday, to project a positive image of the country as welcoming and open.
Russian police usually publish information regularly about crimes including robberies and murders, and also publicise the detention of everyone from suspected murderers to suspected Islamist militants.
The interior ministry did not immediately respond to a request for comment.
However, Vladimir Vorontsov, who represents the inter-regional police trade union, told Reuters the order was genuine and had been issued by the ministry.
A senior regional police official said the same.
"There is a request from the ministry not to provide the media with negative information and to instead talk about solved (crimes), detentions, and so on," said the official, who declined to be named because he was not authorised to speak to the media.
(Reporting by Denis Pinchuk; Writing by Tom Balmforth; Editing by Andrew Osborn and David Stamp)
