A letter was sent to Kensington Palace, reportedly addressed to Meghan Markle and Prince Harry and containing a white powder, London's Evening Standard reports.
The letter was intercepted before reaching the couple but a full security scare was sparked over fears it could contain anthrax.
Ms Markle and Prince Harry - who are due to Wednesday on May 19 - have been informed of the incident, London's Evening Standard newspaper reports.
It says the substance "was tested and confirmed as non-suspicious".
That powder was also found to be non-toxic.
The force said Thursday that detectives are investigating an offense of malicious communication in relation to the package. "No arrests; inquiries continue".
Officers from the Met's counter-terrorism command were called in after the letter was received at St James's Palace, for sorting, on February 12, the Standard said.
Last month, white nationalist and Wisconsin Republican Congressional candidate Paul Nehlen was banned from Twitter over racist imagery of the actress, The Sun reported.
Police are now investigating to determine whether the incidents are linked.
The carriage procession will travel along a route through the streets of Windsor before heading back to Windsor Castle.
Contacted by AFP, Prince Harry's press service at Kensington Palace declined to comment on the report.
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