The letter, addressed to her and fiancé Prince Harry and understood to contain a racist message, led to a security scare, with specialists rushed in to check the powder.
Measures already in place meant the package was intercepted before it reached the couple. Meghan, 36, and Harry, 33, are understood to have been informed.
Officers from the Metropolitan Police’s counter-terrorism command were called in after the letter was received on February 12. It was delivered to St James’s Palace for sorting. Analysis of the powder found it was harmless.
On February 13, police revealed a package containing white powder had been sent to Parliament, reportedly to the office of Home Secretary Amber Rudd.
The material was also found to be harmless. Police are believed to be examining whether the incidents are linked. There have been no arrests.
The palace letter is being played down officially by police but it has put the Met on high alert before the wedding in Windsor in May.
Security for the day is under constant review, with potential threats ranging from a terror attack to that posed by obsessed individuals.
Thames Valley Police has bought a net of spikes which can stop a vehicle weighing up to 17 tonnes and be deployed in less than a minute.
Meghan and Harry are due to ride around a public route in a carriage after marrying at St George’s Chapel in Windsor Castle on Saturday May 19.
They will pass along a route including Castle Hill, High Street, Sheet Street, Kings Road, Albert Road and Long Walk then return to the castle.
There are no plans to change any of the details of the wedding, which is being paid for by the royal family.
The anthrax scare is the first security alert surrounding Harry’s fiancée, who will become an official member of the royal family after the wedding but already has 24-hour protection.
She has been assigned a team from the Met’s royalty and specialist protection command.
The US former actress will have been briefed on security and how she should react in a threatening situation. She and Harry announced their engagement last November.
Cases of hoax letters involving white powder have soared since 2001, when anthrax attacks in America left five people dead.
This month police in Washington DC began investigating after a substance, thought to have been baby powder, was sent to the office of ex-president Barack Obama.
Anthrax is an acute infectious disease caused by spore-forming bacteria and can be fatal.
Flu-like symptoms and distinctive lesions usually appear within seven days.
Infection can occur by breathing the bacteria, ingesting it or through skin contact.
The disease can be weaponised as a powder but is possible to treat with antibiotics.
In October a man aged 31 allegedly called for attacks on Harry’s nephew Prince George. He faces trial in April.
The Met said: “Police are investigating after a package containing a substance was delivered to St James’s Palace on Monday, 12 February.
The substance was tested and confirmed as non-suspicious. Officers are also investigating an allegation of malicious communications which relates to the same package.”