Open data published by Nasa was used to make the map, which has been posted on the OS Flickr account.
This is the first time that OS has produced a map of territory from another planet.
It has also been printed in a one-off edition for a British scientist helping to plan the landing of a rover on Mars in 2019.
"It was a little hard at first to actually understand the data itself in terms of things like the elevation and the scale and so on," said the OS cartographer behind the map, Chris Wesson.
"But actually the physical process was almost identical to what was used to make an Earth map, or any OS map."
The map itself covers roughly 10 million sq km (3.8 million sq miles) - or about 7% of the total Martian surface.
Mr Wesson said he could imagine a future astronaut using a copy of the map - perhaps in digital form - when exploring Mars.
"You have these large areas that looked flat but they're actually really rocky and uneven surfaces - that was the most difficult bit of the map, to try to show that but put it in proportion to these huge craters," he told the BBC.
OS was asked to make the map by Dr Peter Grindrod, a British scientist at Birkbeck, University of London.
Dr Grindrod is helping to plan the landing of the European ExoMars rover in early 2019.
"He's given extremely good responses so far," said Mr Wesson.
Dr Grindrod said he had always admired OS maps and pointed out that they are good at including lots of information in an easily read format.
"It's wonderful to see the same style applied to Mars, and especially such a fascinating region," he said.
British mapping agency Ordnance Survey (OS) has released an easy-to-read map of terrain from the planet Mars.