The blockage caused a pileup of at least 100 vessels seeking to transit between the Red Sea and Mediterranean, according to ship brokers and mapping data compiled by Bloomberg.
Vessels to the north and south waited as the tugs tried to free the ship.
It usually takes between 12 and 16 hours for a ships to transit through the canal.
Photographs released by the SCA also showed excavators onshore digging soil from the canal's bank, with the earth-moving equipment dwarfed by the giant hull towering above.
Cargo ships and oil tankers appeared to be lining up at the southern end of the Suez Canal, waiting to be able to pass through the waterway to the Mediterranean Sea, according to MarineTraffic data.
As of early Wednesday morning, live satellite maps from MarineTraffic.com show the Ever Given still wedged across the canal and surrounded by a half dozen tug boats working to free it. "There have been no reports of injuries or pollution".
Julianne Cona, who was aboard the Maersk Denver directly behind the Ever Given, shared an image of the vessel on Instagram. "Looks like we might be here for a little bit".
Around 10 per cent of the world's trade flows through the waterway and it remains one of Egypt's top foreign currency earners.
"Ship in front of us ran aground while going through the canal and is now stuck sideways", she wrote on Instagram.
The ship is en route to Rotterdam, Netherlands, from the Yantian district of China, according to Vessel Finder.
Tugboats are desperately trying to shift the massive vessel as a massive backlog of ships accumulates at the mouth of the Red Sea, and the Great Bitter Lake.
The 400m-long Ever Given cargo ship, which flies under the flag of Panama, ran aground and turned inside the canal as it travelled north towards the Mediterranean Sea.
It has been a boon for Egypt's struggling economy in recent years, with the country earning $5.61 billion in revenues from the canal in 2020. In 2015, the government of President Abdel-Fattah el-Sissi completed a major expansion of the canal, allowing it to accommodate the world's largest vessels.
In February, Sisi ordered his cabinet to adopt a "flexible marketing policy" for the canal in order to cope with the economic downturn caused by Covid-19. Thousands of ships travel through the canal every year; more than 18,000 ships traveled the canal in 2018.
Most of the cargo travelling from the Gulf to Western Europe is oil.
In the opposite direction, it is mostly manufactured goods and grain from Europe and North America headed to the Far East and Asia.