The 25,000-tonne Bunga Terati Satu has been holed in the bow section, but there are no reports of any pollution.
One report said there was no pilot on board when it hit Sudbury Reef, off Queensland.
AFP news agency said the pilot had been dropped off in Cairns as the vessel was entering an area where compulsory pilotage was not required.
The ship is the biggest of its type to hit the 2000km Great Barrier - the largest complex of coral reefs in the world.
Officials have said it may not be refloated until next week because of unfavourable tides.
Conservationists immediately demanded a ban on any shipping in the area that posed a danger to the reef's delicate ecosystem.
Damage
The 184m long ship, owned by Malaysian International Shipping Corp Bhd, was en route from Singapore to Sydney when it ran aground.
Queensland transport department officials said it had suffered damage to at least the port side of its hull.
But Queensland Transport Minister Steve Bredhauer said they had established the cargo was secure.
"The entire cargo on the vessel is fully containerised and all of those containers are intact and secure," he added.
"There are no reports at this stage of any marine pollution problems."
Ban
Conservationists called on Friday for ships carrying dangerous cargo to be banned from the reef.
The Great Barrier, which is listed as a world heritage site, runs along the Australian coast and extends nearly as far as Papua New Guinea.
"Accidents will happen if we allow this sort of shipping in the reef waters," Australian Conservation Council spokesman Don Henry told Australian Broadcasting Corporation radio.
"The clear answer is that the reef is so important we must ban dangerous shipping."