Travel restrictions apply to
all third-country citizens*, irrespective of whether the traveller needs a visa or can travel without a visa to the Schengen area. There are, however, certain
exemptions from the travel restrictions that are addressed more closely below.
Travel restrictions do not apply to:9. Foreign citizens who can provide appropriate proof of vaccination against COVID-19 or a prior COVID-19 infection that fulfills requirements set forth by the Chief Epidemiologist.FROM 1 JULY – certificate is valid when
14 days have passed from the second dose (or 14 days from Janssen/Johnson & Johnson dose)
https://www.logreglan.is/english/regarding-travel-restrictions-to-iceland-as-a-result-of-covid-19/