Officers from the Metropolitan Police's counter-terrorism command were called in after the package was received on February 12 at a sorting office in St James's Palace in central London.
"The substance was tested and confirmed as non-suspicious," police said in a statement.
Enquiries continue and there have been no arrests, it added.
Contacted by AFP, Prince Harry's press service at Kensington Palace declined to comment on the report.
"Police are investigating after a package containing a substance was delivered to St James's Palace on Monday, 12 February," the police statement added.
"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," it said.
The Evening Standard newspaper reported police were examining whether the incident was linked to a package containing white powder that was sent to Britain's parliament on February 13.
The couple are due to marry in Windsor on May 19.
When their relationship was first revealed in 2016, Harry issued a strongly-worded statement against media harassment of his mixed-race girlfriend.
Harry's communications secretary Jason Knauf said at the time that Markle had been the subject of "a wave of abuse and harassment."
"Prince Harry is worried about Ms Markle's safety and is deeply disappointed that he has not been able to protect her," Knauf said then.
