The five-time darts world champion and Sky Sports commentator also posted homophobic tweets.
In one post, he likened being gay with being a paedophile and wrote: “Might be a looney but if some football coach was touching me when i was a kid as i got older i would have went back and sorted that poof out.”
“U got to sort him out when u get older or don’t look in the mirror glad i am a dart player proper men.”
He added: “Bet the rugby boys are ok ha ha.”
Twitter users reacted angrily to the comments, labelling the sportsman “disgusting” and “homophobic”.
Other users said they would be returning the player’s branded darts equipment in protest at his comments.
The 59-year-old later stated that rugby players would not have been victims of child sex abuse like footballers, because “footballers wimps”.
He wrote, “sorry meant paedo not poof” appearing to confirm he had confused being gay with being a paedophile.
Hours after posting the series of abusive Tweets they had been removed from his account.
Sky has now confirmed that Mr Bristow, who was awarded an MBE in 1989 for his services to sport, will not be appearing on the network as a pundit again.
“He was a contributor to our darts coverage in the past but we will not be using him in the future,” said a Sky spokeperson.
Several former footballers have waived their right to anonymity in order to go public and raise awareness of alleged historical abuse in football, a step which has won praise from politicians, sport administrators and abuse charities.
Steve Walters, one of the ex-players to have spoken out about his abuse at the hands of convicted paedophile and former Crewe coach Barry Bennell, responded to Bristow, saying on Twitter: “Disgusted with Eric Bristows remarks tonight #stoneagementality.”