The game features cards with a series of quiz questions, but some of the answers given are incorrect.
One answer claims the moon is 225 miles away from the earth - instead of about 238,900 miles.
Manufacturers Paul Lamond Games said they "unreservedly apologise" and added replacement cards would be issued.
It is understood at least six of the 50 answers in one round of the game - which costs Â£19.99 - are incorrect.
One answer placed Stonehenge in Somerset instead of Wiltshire and a maths question suggested two cubed was bigger than three squared.
It also said Albert Einstein died in 1949 instead of 1955 and gave the number of Coronation Street episodes to date as 8,000, when the actual figure is more than 9,000.
One customer who bought the game told The Sun: "I couldn't believe it, the answers are so ridiculous... [but] the kids won't accept the game could possibly be wrong."
A representative for Paul Lamond Games told the BBC: "We have been made aware of some mistakes with the answers to the questions within the first production run of this game."
"These have now been corrected and we would like to unreservedly apologise for these errors.
"Any affected customer can email us stating their name and full address and we will send out a replacement set of corrected cards free of charge."
The company's email address is available on their official website.
Ant & Dec - whose full names are Anthony McPartlin and Declan Donnelly - have hosted Saturday Night Takeaway on ITV since 2002, although the show took a four-year break from 2009.
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The makers of Ant & Dec's Saturday Night Takeaway board game have apologised after it was found to have several errors.