The England international was charged with improper conduct by the FA after he acknowledged a comment on Twitter that referred to the Chelsea defender as a 'choc-ice'.
Ferdinand – who denied the charge – attended a secret hearing in London last Friday.
The FA said in a statement: 'Manchester United's Rio Ferdinand has been fined £45,000 after an independent regulatory commission found proven a charge of improper conduct in relation to a comment posted on Twitter.
'The commission decided that the comment was improper and brought the game into disrepute. In addition, the commission found that the breach included a reference to ethnic origin, colour or race.'
Ferdinand's former England team-mate Cole appeared as a witness for John Terry when the Chelsea defender appeared in court during the summer charged with making racist comments to the United man's younger brother Anton.
Terry was cleared of the charges but soon after Ferdinand Snr appeared to endorse a tweet describing Cole as a 'choc ice, a slang term perceived as meaning black on the outside and white on the inside.
Ferdinand tweeted: 'I hear you fella! Choc ice is classic hahahahahaha!!'
Users began discussing the comments and reacting to them and Ferdinand wrote: 'And if I want to laugh at something someone tweets....I will! Hahahahaha! Now stop getting ya knickers in a twist!'