Creator Seth MacFarlane has also criticised an "abhorrent" edit of the show that is circulating on the internet.
The episode, Turban Cowboy, originally went out on March 17 and shows a sports presenter asking the show's main character, Peter Griffin, about his performance at the marathon.
A flashback scene then shows Peter drunkenly mowing down runners with his car to win the race.
"I'll tell ya, Bob, I just got in my car and drove it," says Peter. "And when there was a guy in my way, I killed him."
Three people were killed and more than 170 others injured after two explosions near the finish line at Monday's Boston Marathon.
Fox has confirmed the episode will not be shown again on the network in the immediate future and confirmed it had been taken down from Fox.com and Hulu.com.
In a separate scene later in the episode, Peter befriends a terrorist who - unknown to him - is planning to blow up a bridge.
When Peter uses a mobile phone he unwittingly detonates two bombs and explosions and screams are heard.
However, an unauthorised clip on the internet has put the two scenes back to back, making it seem like the explosion occurs at the marathon.
"The edited 'Family Guy' clip currently circulating is abhorrent," Seth MacFarlane tweeted. "The event was a crime and a tragedy, and my thoughts are with the victims."
MacFarlane also voices Peter's character in the hit animated show, which has run for over 200 episodes and also features the voice of actress Mila Kunis.