I mean, there's a long precedent of restricting free speech in the public interest. The classic example of shouting fire in a public theater comes to mind: the speech causes imminent danger to the theater occupants, and the courts have ruled that the rights of the public to safety outweigh the rights of the individual to say whatever they'd like.

The question with fake news becomes: what is the damage that this type of speech causes to the public? This is a really difficult question to answer, especially since we're only starting to notice the effects on our political system. If this damage is too great, there would be justification to restrict it in the public interest.

Of course, the people who end up making these determinations may also have conflicting political incentives, which makes this a very delicate situation to tackle in as broken of a political environment as we have in the US.