Iceland is part of the common European market and therefore residents and businesses within the European Union and EFTA enjoy in most cases the same rights to invest as locals.There are though some sectors that this does not apply to.  

Companies that work in the fishing industry and within the Icelandic fisheries jurisdiction need to be wholly owned by Icelandic individuals or legal entities that are controlled by Icelanders. The ownership of foreign entities must not exceed 25% and up to 33% in certain circumstances. Only Icelandic citizens or entities are permitted to own energy exploitation rights relating to waterfalls and geothermal energy for other than domestic use. The same applies to businesses that produce or distribute energy. 

Foreigners can own 49% or less in Icelandic airline companies. The Ministry of Industries and Innovation must provide special permission if a foreign state, municipalities or other foreign authorities wants to invest in Icelandic companies. An individual domiciled within the EEA or OECD is allowed to run a business in Iceland or be a partner. However, individuals and companies outside the EEA and OECD must get special permission by the Ministry of Industries and Innovation.  Private individuals may purchase real property if they are either Icelandic citizens or have their legal residence in Iceland. Partners in businesses also require domicile in Iceland for at least 5 years in order to purchase a real property.