The scenes, which were unearthed by a member of the public, led to condemnation on social networking sites.
Miqdaad Versi, Assistant Secretary General of the Muslim Council of Britain, wrote on Twitter: "[I] have no idea what went through the producers' minds when they thought this was a good idea."
Mr Versi identified one page as containing verses 13 to 26 of chapter 67 of the Quran, which deals with issues such as the origins of existence, and the punishments meted out to non-believers.
In a statement, HIT Entertainment, which also owns brands such as Thomas the Tank Engine and Bob the Builder, said: "It has been brought to our attention that in an episode of Fireman Sam an image of the Quran is briefly depicted. The page was intended to show illegible text and we deeply regret this error.
"We will no longer be working with the animation studio responsible for this mistake.
"In addition, we are taking immediate action to remove this episode from circulation and we are reviewing our content production procedures to ensure this never happens again."
In 2012, one of the creators of Fireman Sam, David Jones, was held at Gatwick Airport, after making a comment about a Muslim woman who was wearing a veil.