A package containing a substance which was sent to St James’s Palace is being treated as a racist hate crime, Scotland Yard said.
Police have launched an investigation after the letter was delivered to the royal residence in central London on February 12.
The substance was tested and not found to be suspicious, the Metropolitan Police said.
No arrests have been made.
The Metropolitan Police said: “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 matter is being investigated by officers from the Met’s Counter Terrorism Command.”
St James’s Palace is home to several members of the Royal Family and their household offices.
Ms Markle, whose father is Caucasian and mother is African-American, said in a BBC interview in November that it had been “disheartening” to receive negative attention about her ethnicity in the early period of her relationship with Harry.