The Moonfruit service lets customers easily build templated websites.
But the company said it had been threatened with a cyber-attack and had decided to make its customers' websites unavailable for up to 12 hours to make infrastructure changes.
One business owner told the BBC it was very bad timing.
On Thursday, 10 December, the company said it had been hit by a distributed denial of service (DDoS) attack.
Attackers bombarded the company's computers to overwhelm them with traffic, so they could not serve its legitimate users.
The company consequently told customers it had decided to take websites offline for up to 12 hours starting at 10:00 GMT on Monday.
Film-maker Reece de Ville said: They have been slow to communicate via their website what is going on.
I'm going to have hundreds of people finding my site today but not being able to access it.
I could be losing out on a lot of money from potential clients, and they may not come back if they think the company has gone.
It's incredibly bad timing, especially for businesses selling Christmas cards and gifts on their website.
In an email to its customers, the company apologised for giving them short notice that their websites would be offline.
We have been working with law enforcement agencies regarding this matter and have spared no time or expense in ensuring we complete the work as quickly as possible, the company's director, Matt Casey, said in a statement.
The BBC has invited Moonfruit to comment.
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