If it’s officially declared, then it’s not just de facto – but no, a president would not be required to go as far as a declaration of martial law.
Presidents have taken “emergency powers” into their own hands before – from Thomas Jefferson to Abe Lincoln to Franklin Roosevelt to George Walker Bush. All of these were accused of violating the Constitution but, for various reasons, the accusations did not leave us with a body of law that rules out seizure of “emergency powers” at the federal level.
In current circumstances, if Trump were to issue a “national stay-at-home order” or some such thing, and if it were to be challenged, his DOJ would have to defend it in the courts. You can probably figure out how that should go, and also how it would go.