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.
Follow us on Facebook, on Twitter @BBCNewsEnts, or on Instagram at bbcnewsents. If you have a story suggestion email entertainment.news@bbc.co.uk.

They include a new water sports park, railway station and a sliproad from the M77.
The City Deal scheme will see eight council areas around Glasgow receive about £1bn from the UK and Scottish governments.
The councils also have the power to borrow extra cash.
The Glasgow and Clyde Valley City Deal involved massive investment by both the Scottish and UK governments last year.
Eight councils - Glasgow, East Renfrewshire, Renfrewshire, Inverclyde, North and South Lanarkshire and East and West Dunbartonshire - are involved.
The City Deal scheme will see Westminster and Holyrood give £500m each in additional grant funding to the eight council areas.
The councils will supplement this by borrowing £130m.
Councillors from across all eight areas will meet to discuss some of the schemes.
Several of the projects being discussed later are in East Renfrewshire, where £44m is expected to be invested over the next few years, with much of the money coming from the City Deal funding.
One is a water sports park at the Dams to Darnley Country Park. It would open in 2017 and include a centre offering wakeboarding, the fastest-growing extreme sport in the world.
A new railway station in Barrhead and sliproad from the M77 would serve an area which could become one of East Renfrewshire's fastest growth areas. The council expects 1,000 new homes to be built there.
Another project would transform the Levern Works site in Barrhead. A site formerly occupied by Nestle, where pet food was once made, would be cleared. The site will then be marketed for development for a range of uses that will bring new jobs to Barrhead.
A wide range of other infrastructure projects across the eight council areas will also be discussed.
The makers of Ant & Dec's Saturday Night Takeaway board game have apologised after it was found to have several errors.
[NEXT_CONCEPT]
Some of the first projects to be funded by the City Deal programme for the west of Scotland are to be discussed by councillors.