You need a visa for Antigua and Barbuda if you have an Icelandic passport
Visa options for Antigua and Barbuda
Electronic visitor visa
Travellers need a visa to visit Antigua and Barbuda for Business or Tourism. Travellers who have a valid visa or residence permit issued by Canada, the United Kingdom, or the United States or who have a valid visa issued by a Schengen member state to visit are eligible for a visa on arrival. Otherwise, an Antigua and Barbuda eVisa is the fastest and easiest way of obtaining a visa for Antigua and Barbuda because travellers can submit their applications and supporting documents online. Once the application is approved, travellers receive their eVisa confirmation electronically. Travellers must have proof of onward travel.