(The ultimate wisdom of his position is neither endorsed nor condemned by this post.)
If, for the purpose of argument, we stipulate as fact that the fears are overblown, he might be able to successfully attack this order as "unnecessary" under that law, but that sounds iffy, and the health officers will no doubt be afforded substantial deference.
A better avenue for attack would be via the US Constitution and its basic protections for civil rights, liberty, and freedom of assembly. The Fifth Amendment specifically applies, forbidding that anyone "be deprived of life, liberty, or property, without due process of law." The regional lockdown affects ~7 million people, to contain a disease that has affected ~300 (?) known patients (please correct me if this is badly wrong) so this lockdown may be serving a compelling government interest, but it is probably not doing so via the least restrictive means available, which would usually be the standard for abrogating civil liberties. It's a meaningful case, at least.
Whether he wins or loses such a hypothetical case, though, it would leave things clearer than the situation which jgalt observes nearby:
> it seems more like Musk is the sort to get sued, not the one to be suing
Better to be fighting in the courts from the start, rather than being confronted by the sheriff partway through the workday.
These companies are very unlikely to do so without being forced.
"Honda Plans to Shut Down North American Plants for Six Days Due to Virus Concerns, Demand Decline"
https://www.wsj.com/articles/honda-plans-to-shut-down-north-...
"UAW, Auto Makers Agree to Partial Plant Shutdowns to Curtail Coronavirus. Ford temporarily closes Chicago factory for virus-related parts shortage... The United Auto Workers and Detroit car companies reached agreements on coronavirus-mitigation efforts that for now will avoid a two-week shutdown of U.S. factories."
https://www.wsj.com/articles/uaw-presses-auto-makers-to-clos...
"Volkswagen, Airbus Halt European Production Amid Wave of Factory Closures" (Europe not US) https://www.wsj.com/articles/volkswagen-airbus-halt-european...
There's a _huge_ negative publicity risk here, depending on how things unfold.