"Whilst not everyone may see Christmas as a religious holiday, it should be respected as such," the petition says.
A letter will be sent to the Prime Minister Theresa May with the petition attached. It will call for her to ban shops from opening on 26th December.
"Forget making money for one day, let's concentrate on making more memories with the ones we love," she will be told.
The petition quickly went viral on social media with it being shared by thousands of people.
"We're really delighted people are doing that because it's really important there is a clear signal that consumers and ordinary people are concerned about these issues," said John Ashcroft from the campaign group Keep Sunday Special.
In previous years some major stores have agreed to close on Boxing Day. In 2015, John Lewis decided not to open its flag ship Oxford Street branch. Several Marks and Spencer's stores across the UK also remain closed, although the number deciding to open increases every year.
The petition says: "Retail workers, who work so hard on the run up to the big day, [should be] given some decent family time to relax and enjoy the festivities like everyone else.
"Most retail workers are on the go up to Christmas Eve, then back on Boxing Day. Sometimes they have no choice.
"We managed 30 and 40 years ago when shops were sometimes shut for a whole week. Let's get back to the way it was."
Ashcroft, whose group Keep Sunday Special led a successful campaign against government plans to relax trading restrictions on Sundays said: "Over Christmas shop workers may be working right up to the end of Christmas Eve, you've then got to be in early on Boxing Day so it's a very short time with family and many shop workers are parents with children."
He accepted stores only opened on the 26th because there was a demand but warned shoppers to "recognise that the choices we make have an impact on other people".
He said it was a misconception that staff choose to work on Boxing Day because of premium payments.
"Shop workers are under pressure," he stressed.
John Ashcroft speaking to Premier's Antony Bushfield:
