The Met Police tested the substance and said it was not harmful. No arrests have been made and inquiries are ongoing.
The Evening Standard reports the letter was addressed to Prince Harry and Meghan Markle.
It was received on February 12, the day before a package containing white powder was sent to Westminster.
It is alleged the substance sent to St James's Palace was also white powder. Officers are looking into whether or not the two packages are linked.
A spokesman said: "It is being treated as a racist hate crime. The matter is being investigated by officers from the Met's Counter Terrorism Command."
Prince Harry condemned the "the outright sexism and racism of social media trolls" Ms Markle was subject to when they made their relationship public in 2016.