An investigative commission had concluded that the company "was in part responsible" for Friday's tragedy, which killed at least 107 people and injured almost 400 during a severe thunderstorm accompanied by violent winds.
The company had not "respected the norms of safety" at the site, the official Saudi Press Agency (SPA) said.
The firm's executives have been forbidden from leaving the kingdom pending the completion of legal action against the company, SPA said.
The construction firm belongs to the family of the late Al-Qaeda leader Osama bin Laden.
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It had been working for four years on a 400,000-square-metre (4.3-million-square-feet) enlargement of the Grand Mosque, to accommodate increasing numbers of pilgrims.
That is the equivalent of more than 50 football pitches, and will allow the complex -- Islam's holiest site -- to accommodate roughly two million people at once.
After visiting the scene of the tragedy Saturday, Salman vowed to reveal what happened.
It was the worst accident in a decade surrounding the hajj, which begins today and is expected to draw about two million faithful from around the world.
Saudis, Iranians, Nigerians, Malaysians, Indonesians and Indians and were among the dead.
Officials say the tragedy will have no effect on preparations for the hajj, one of the world's largest religious events.
An engineer with Saudi Binladin Group told AFP Saturday that what happened was an "act of God" and not the result of a technical fault.
The crane, like many others on the project, had been there for three or four years without any problem, he said\.
"I can only say that what happened was beyond the power of humans. It was an act of God and, to my knowledge, there was no human fault in it at all."
The engineer said the crane was the main one used on work to expand the tawaf, or circumambulation area around the Kaaba -- a massive cubed structure at the centre of the mosque that is the focal point of Muslim worship.
"It has been installed in a way so as not to affect the hundreds of thousands of worshippers in the area and in an extremely professional way," he said of the crane.
The crane's heavy hook, which is able to lift hundreds of tonnes, began swaying and moved the whole crane with it, toppling into the mosque, the engineer explained.