Rabie said that the vessel's passage on Friday was overseen by "senior" guides of the authority.
The vessel was seen sailing in open waters accompanied by Egypt-flagged tugboats in aerial video footage posted on the SCA's Twitter account.
The Ever Given -- a behemoth with deadweight tonnage of 199,000 -- got stuck diagonally across the canal during a sandstorm on March 23.
A round-the-clock salvage operation took six days to dislodge it.
After it was freed, Egypt seized the ship and demanded compensation from owners Shoei Kisen Kaisha for lost canal revenues, salvage costs and damage to the waterway.
The Taiwanese-operated vessel steamed out of the Suez last month after the Japanese owners reached a compensation deal with Egypt.
The terms of the deal were not disclosed publicly but Egypt had originally demanded more than $900 million in compensation, which it later reduced to $550 million.
One employee of the SCA was killed during the rescue operation.
In May, Egypt's President Abdel Fattah al-Sisi approved a two-year project to widen and deepen the southern part of the waterway where the ship ran aground to avoid any repetition of the crisis.
Egypt, which takes a toll from ships traversing the canal, said the crisis cost it as much as $15 million per day, while maritime insurers estimated the hit to world trade to be in the billions.
Last month, the SCA's Rabie said the canal netted Egypt a record $5.84 billion in the last tax year, despite the impact of the coronavirus pandemic on world trade plus the cargo ship's blockage.