The letter was received this month at St James Palace in central London. The powder inside was found to be harmless after being examined by experts.
The couple are due to be married in May and the letter was received at the palace shortly before a package containing white powder also prompted a scare at the Palace of Westminster.
The Evening Standard newspaper said the royal couple had been informed of the suspicious package.
The police inquiry is trying to determine if the same person or people were responsible for the sending both letters.
Anthrax can be weaponised in powder form and is potentially deadly. But there have been a number of scares where harmless white powder has been sent to prominent people.
Scotland Yard ssaid in a statement: “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. No arrests; inquiries continue.”
A spokesperson for St James Palace said they would not comment and it was a matter for the police.