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Counter-terrorism officers are also treating a letter which accompanied the package as a racist hate crime, the Metropolitan Police said in a statement.
The package was sent to St James's Palace on Monday and police later confirmed the substance it contained - reportedly a white powder - was non-suspicious.
"Officers are also investigating an allegation of malicious communications which relates to the same package, and it is being treated as a racist hate crime," the police statement said.
The London Evening Standard newspaper reported that the package had been addressed to Harry and Markle, his actress girlfriend who he is to marry in May. A spokeswoman for the prince, Queen Elizabeth's grandson, said they had no comment on the reports.
In a rebuke from his office to the media in 2016 over intrusion into his fiancee's private life, Harry referred to the racism that had been directed at Markle, whose father is white and mother is African-American.
Asked about the scrutiny of her ethnicity in a TV interview after their engagement was announced, Markle said: "Of course it's disheartening, you know it's a shame that that is the climate in this world to focus so much on that."
The incident at the palace occurred the day before police were called after white powder was sent to an office in Britain's parliament. That too was found to be harmless.
Harry, the younger son of heir-to-the-throne Prince Charles, and Markle, best known for her role in the U.S. TV legal drama "Suits", will marry at a ceremony at the queen's Windsor Castle home on May 19.
The couple will celebrate their wedding day with members of the public by taking a carriage ride through the town, although security is likely to be high after Britain suffered four deadly attacks blamed on terrorism last year.