"We will not be taking any orders in the meantime. Sincere apologies for the inconvenience."
The blaze started at the company's main warehouse in Barnsley, South Yorkshire, on Friday night and raged into the early hours of Saturday.
More than 60 firefighters were called to put out the flames that spread from the second floor up through the five-storey building.
Fortunately it is on an industrial estate away from homes but a road near the site was closed.
A spokesman for South Yorkshire Fire and Rescue said teams stayed on the site on Saturday morning to ensure remaining "hot spots" did not reignite.
He added: "At its height, the fire was tackled by 10 fire engines, an aerial ladder platform and a high volume pump.
"The warehouse was more than 60,000 square metres in size. The fire involved several floors of the building and fire crews worked hard to quickly bring the blaze under control."
The cause of the blaze is being investigated.
Founded in 2000, Asos has become one of the UK's largest online fashion retailers, with over 60,000 product lines and websites pushing into the global market shipping to 109 countries.
Its website describes the damaged warehouse as "the size of six football pitches, so pretty huge".
It adds: "Every one of our products comes here and is checked, picked and packed before making its way by air, land or sea, to be delivered."
For safety reasons, employees had not been able to enter the warehouse to check which orders were damaged and see how deliveries will be affected.
- The Independent