You need an embassy visa for Faroe Islands if you have an Indian passport
Visa options for Faroe Islands
Visitor visa
Travellers need a visa to visit Faroe Islands for Business or Tourism. A paper or embassy visa is the only visa available for travellers visiting Faroe Islands. The visa is typically a stamp or sticker added to the passport. Travellers must obtain this visa from a local embassy, consulate or visa center before travelling.