Foreign ownership of the exploitation rights of hydro and geothermal energy and investment in energy production and distribution by foreign persons is prohibited. Individuals and legal persons domiciled in an EEA or EFTA state or in the Faroe Islands are exempted.
"Article 4:
Investment by non-residents in business operations in Iceland is subject to the following restrictions: [...]
2.Icelandic citizens and other Icelandic persons may only own hydropower and geothermal rights other than for domestic use. The same applies to companies engaged in energy production and distribution. [Individuals residing in another Member State of the Agreement on the European Economic Area, another Member State of the Treaty establishing the European Free Trade Association or the Faroe Islands and legal entities domiciled in another Member State of the Agreement on the European Economic Area, another Member State of the Treaty establishing the European Free Trade Association] have the same rights. Investment agreements between Iceland and countries outside the European Economic Area may stipulate that individuals residing there or legal entities resident there also have the same right, provided that such agreements are submitted to Althingi for approval by a parliamentary resolution.
Non-residents who acquire ownership and use rights over real estate in accordance with the provisions of the Act on Ownership and Use Rights of Real Estate may use geothermal energy for direct use in their business activities within the limits set out in the Energy Act.
[...]
For the purposes of this Article, an Icelandic person refers to the state treasury and municipalities, as well as institutions, companies and funds in this country wholly owned by them, Icelandic citizens who are domiciled in this country and legal entities that are domiciled in this country and are wholly owned by owned by public entities in this country, Icelandic citizens who are domiciled in this country or other legal entities that are domiciled in this country and are wholly owned by Icelandic citizens who are domiciled in this country. For the purposes of this Article, an Icelandic legal entity refers to a legal entity domiciled in this country, regardless of the form of operation or ownership. A legal entity is considered to have a domicile in this country if it is registered in this country, if it considers its domicile in this country according to its articles of association or if its actual executive board is in this country. [...]" (Act on Investment by Non-residents in Business Enterprises (34/1991), last amended 24 December 2019, Article 4 [google translation])
Act on Investment by Non-residents in Business Enterprises (34/1991), last amended 24 December 2019, Article 4
[<a href="https://www.althingi.is/lagas/nuna/1991034.html">Act</a>]