Walkers on Boothferry Road is set to close by the end of this month the Courier discovered this week.
Graham Kerr, managing director of St Albans-based Top Ten Holdings, which has run the business for the last two years, said: "The closure really comes with the impact of the impending smoking ban.
"It will tip it from being a central source of business to one that just doesn't work anymore.
"Goole is one of a number that we are closing, we have three so far, apart from Goole.
"This is happening right across the industry."
He could not confirm how many staff would suffer as a result of the closure.
Top Ten Holdings Plc operate bingo halls, amusement arcades and snooker clubs across the country.
Goole MP Ian Cawsey said: "Having visited Walkers on several occasions over the years I will be sorry to see it go. However, I am not sure that a decision to close now some months before the smoking ban even begins means it is simply because of that. "My understanding is that numbers at many bingo clubs across the country have fallen for all kinds of reasons, not least the ability to play online at home for bigger prizes.
"Indeed clubs in Scotland, where smoking has been banned for a year now, say that the installation of covered smoking facilities outside the club did nothing to bring people back."
He added: "However, the real loss is not the bingo playing but the social side of Walkers where people could pop out and have a chat with others whilst enjoying the game. I hope that other social clubs and community centres in the town will continue to offer that environment whilst local people want to spend their leisure time playing bingo."
According to leading gaming company Rank Group plc, the smoking ban which was put in place in Scotland this time last year made trading "difficult".
A spokesman for the company said earlier this month that it was "bracing itself" for the introduction of the smoking ban in England and Wales after sales continued to slide north of the border.
Like-for-like sales at its Mecca Bingo Clubs in Scotland had fallen 15 per cent since smoking was banned in public places.
And there was further bad news for smokers this week with the Chancellor of the Exchequor Gordon Brown's budget announcement on Wednesday that the cost of cigarettes will rise by 11p a packet.
Thinks looked brighter for those who are trying to quit the habit when it was revealed the VAT on nicotine patches and similar products will be cut from 17.5 per cent to five per cent.