The former Manchester United defender described a Twitter user's mother as a "sket" after said user indicated on the social networking website that QPR's centre-backs were no good.
Today, Barton tweeted, "3 games and £25k for a tweet? Come on," which prompted a reply from Ferdinand, who said: "its a Tepid tweet....3games. im not even going to hashtag it!!"
Barton continued his conversation with Ferdinand by saying: "I have said way worse I am sure. Don't understand how you can be banned from football. It's nothing to do with it.
"It's an absolute disgrace. They have set a dangerous precedent now. Looking forward to seeing them police this? #muppets."
The midfielder then addressed his 2.75 million followers by tweeting: "Can someone from the @FA send me a list of offensive, ban incurring words that I can't use online and the requisite bans attached to each."
It has not yet been confirmed whether Ferdinand will appeal the suspension.