The majority are likely to be older people, according to the Office for National Statistics, with charity Age UK saying many are happy to stay permanently offline.
The ONS asked people aged 16 and over in North Yorkshire whether they had used the internet in the last three months.
Of those surveyed, 10% said they had not recently been online, which amounts to an estimated 48,000 residents.
The ONS said over-75s make up more than half of the 4 million people in the UK who have never used the internet.
But the number of older people regularly using the internet is rising rapidly, closing the age gap with younger users.
Internet use across all ages has increased considerably since 2013, when just 83.3% of people in the UK were frequent users, compared with 91% today.
The majority of adults in North Yorkshire, 90%, use the internet regularly - in line with the UK average.
And usage has risen considerably since 2013. That year, 83% of adults were regularly on the web.
Age UK said increasing internet use among older people is a good thing, but added that a substantial group of pensioners “are not online, and never will be”.
The charity said older people are also more likely to stick to a few online activities, like checking emails or searching for information.
Only around a quarter of over-65s use social media, compared to 96% of 16 to 24-year-olds.
Charity director Caroline Abrahams said: “Lack of knowledge about the internet and digital technology, concerns about security and cost are some of the reasons why older people do not use the internet.
“Others tell us that they have lived life quite happily without computers for many years, so why should they start now?
“While it’s fine to encourage and support older people to get online, those who choose not to, or cannot do so, should not be treated like second class citizens.
“They must still be able to access services and resources in other ways that suit them - telephone, post and in person.”
According to a report by communications regulator Ofcom, the average UK adult spends 3 hours and 15 minutes online every day, or around 50 days per year.
For the first time this year, the ONS compared internet usage in the UK with other EU countries, with the UK coming third overall - behind only Denmark and Luxembourg.