Metropolitan Police officers refused to reveal the contents of the document addressed to the 26-year-old or when they received the complaint.
A Met spokesman said: "I can confirm that officers are investigating an allegation of malicious communication."
Ferdinand is at the centre of a race row involving England and Chelsea captain John Terry, over comments Terry allegedly made to him during a match.
The Met and the Football Association are looking into the claims that Terry racially abused Ferdinand during a match at Queens Park Rangers' Loftus Road ground in October.
The 30-year-old centre-half denies the allegations.