Chelsea captain Terry was found not guilty last month of racially abusing QPR defender Anton Ferdinand, Rio's brother, during a Premier League game on October 23 last year, although he is also now contesting a FA charge over the same incident.
During the trial, Ferdinand appeared to endorse a tweet by another user of the micro-blogging website which described Chelsea defender Ashley Cole, who gave evidence on behalf of Terry in the trial, as a "choc ice".
The term is understood to mean someone who is black on the outside but white on the inside.
The FA felt Ferdinand's support for the controversial tweet brought the game into disrepute and the 33-year-old was given his punishment on Friday.
"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," an FA statement read.
"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."
Cole, who also told the court he was a long-standing friend of the Ferdinand brothers, was accused by one person who sent a tweet to Rio Ferdinand of being a "choc ice".
The person wrote: "Looks like Ashley Cole's going to be their choc ice. Then again he's always been a sell out. Shame on him."
Manchester United defender Rio, who has played with Terry at the heart of England's defence, replied: "I hear you fella! Choc ice is classic! hahahahahahha!!"
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!"