The supermarket chain joins smaller rivals Somerfield and Budgens, which were the first to abandon online shopping in the face of domination from clear market leader Tesco.
Tesco recently announced online sales for the first half of this year of £146m, a 77% increase on 2000.
Safeway had been trialling the Collect service, which allowed customers to order goods online and pick them up from a local store, at eight UK stores since May. At the time of launch, the company said it was not ruling out a move into fully-fledged online shopping, as the front end had been put in place.
However, a spokesman for Safeway said this week that the company had decided not to put further cash into the venture but to concentrate on revamping its existing store portfolio. He said most orders had been received by fax.
"We have latterly been taking e-mail orders but it has never been a pure dotcom business," he said. "There was an enthusiasm for all things dotcom at the time and it was trendy to say you were on the Internet."
While Tesco appears to be running away with the lead in the online grocery shopping market, second placed Sainsbury's has not given up.
It has recently built a new datawarehouse to enable better use of data extracted from its loyalty card and has relaunched its e-commerce site on a new platform, which it said was faster, better and more easy to use.
Meanwhile, the market awaits the entrance of the John Lewis-backed pure play online grocery retailer Ocado, whose launch was due this year but has been put back to the first quarter of 2002.
Ocado, which will use John Lewis' Waitrose brand, will deliver from purpose-built distribution centres. Analysts question the move, pointing out that Tesco.com's success has been based on its method of picking stock from existing stores.