Strict restrictions are in effect since 12 March, 2020 in public transportation that have been further strengthened: only Hungarian citizens and EEA citizens with permanent Hungarian residency may enter Hungarian territory, save for limited exceptional cases.
From 2nd April 2020, only Hungarian citizens and EEA citizens with permanent Hungarian residency may enter the territory of Hungary. An exceptional treatment from these rules may be requested from the traffic police directorate of the Police Headquarters (ORFK) provided that the applicant undergoes medical control which shows no suspected coronavirus infection and (s)he will be registered by the epidemiological authority.
Hungarian citizens and EEA citizens with permanent Hungarian residency travelling from abroad shall undergo medical control at entry and in case of a suspected coronavirus infection, they shall be quarantined. Epidemical authority shall register also persons travelling from the above countries without suspected infection and they shall undergo a so-called domestic quarantine, i.e. may not leave their domicile for 14 days. Those who do not have a permanent residence in Hungary shall either leave Hungary or spend the incubation period in the appointed quarantine. An exemption from the domestic quarantine may be requested only if the person can prove that (s)he is recovered from COVID-19 infection or (s)he has spent at least 14 days in quarantine before entering the country.
Identification documents that will expire during the ‘state of danger’ shall be deemed valid until the 15th day following the cession of the ‘state of danger’, obviously to avoid the related administration at crowded local authorities. Higher education and public education institutions have been shut down. All indoor events with more than 100 guests and outdoor events with more than 500 guests will be banned. Hospital workers, soldiers, police officers and government clerks who are crucial in the defense against the pandemic may leave Hungary only with special permission.
You can read more on restrictions concerning shops and other facilities here.