Seemingly so in Romania, if it threatens national security:
Under certain conditions, fake news may also amount to a criminal offence. In this respect, the Criminal Code provides that dissemination, irrespective of means, of news, data, fake information or fake documents, in full knowledge of their falsehood, if national security is thus endangered, is punished by imprisonment of one to five years. Entities may also be the subject of this criminal offence, if committed in the exercise of their business object, in their interest or on their behalf.
The punishment for entities is a criminal fine computed by multiplying (i) the number of fine-days set by the court (considering severity of the infringement), ranging from 120 to 240 days, with (ii) the amount/ day of the fine, set by the court (based on economic criteria, such as the turnover of the company), ranging from Lei 100 to 5,000. Criminal liability may be aggravated whenever the crime was committed for pecuniary benefits, by elevating the fine-days number by a third (yet without exceeding the overall maximum of 600 fine-days). In addition, it may also attract an ancillary punishment, such as suspension of activity, closure of a working unit of even dissolution of the entity.
This criminal provision underwent constitutional challenge, examining its compatibility with press’ freedom of expression. The Constitutional Court stated that (i) the offence is not confined to solely the press (despite it being the most common vehicle) and (ii) it does not threaten journalistic freedom, since its scope is not to punish mere publication of unverifiable information/ information of uncertain veracity, but information published while fully knowing/ accepting its falsehood.
: The Romanian Constitutional Court’s Decision No. 273 of 20 December 2000
It's unclear to me if courts over there held any Covid fake news to meet this standard though, i.e. threaten national security. There might be some other provision that applies, but I'm rather unclear on that--other answers welcome.
According to IPI, there was however one such explicit law passed in Hungary:
The new law also criminalizes the spreading of “false” or “distorted” information which undermines the authorities’ fight against COVID-19 with fines and up to five years in prison.
There's also mention of an attempt in Bulgaria, but it's not clear if it was successful:
the government used the state of emergency decree to try to amend the penal code and introduce prison sentences for spreading what it deemed “fake news” about the outbreak with up to three years in prison or a fine of up to €5,000.
Regarding Romania, the article says that a decree was passed which allows the takedown of sites with Covid misinformation, but that seems to go under administrative law.
On March 16 the president of Romania, Klaus Iohannis, signed an emergency decree which, among other measures, gives authorities the power to remove report or close websites that spread “fake news” about the virus, with no opportunity to appeal.
I'm not sure how that works with respect to Facebook though. Perhaps the police or some other authorities send a takedown notice for specific articles, as it happens in other countries, e.g. India.