Foreign investment may be blocked if it is considered to threaten national security, public order, public safety or public health, or in the event of serious economic, social or environmental difficulties in particular economic sectors or particular areas, which are likely to be of a lasting nature. Branches of foreign limited liability companies from outside the EEA, EFTA or the Faroe Islands are not allowed unless authorised by the Minister. 
"Article 12:
 If the Minister considers that particular foreign investment threatens national security, public order, public safety or public health or in the event of serious economic, social or environmental difficulties in particular economic sectors or particular areas which are likely to be of a lasting nature, he may suspend such an investment, provided that he announces his decision within eight weeks of becoming aware of the investment in question. In the case of investment by a state entity within the European Economic Area, the provisions of Articles 112 and 113 of the Agreement on the European Economic Area shall be observed, cf. Act no. 2/1993. In the case of an investment by a Member State of the European Free Trade Association, the provisions of Articles 40 and 41 shall be observed in the Memorandum of Association.
The Minister may suspend foreign investment in systemically important companies when such investment involves systemic risk.
The Minister is authorized to stop foreign investment according to Art. Paragraphs 2 and 3 on the basis of suggestions from competent authorities.
[Minister] in the first half of each year, the Althingi shall submit a report on foreign investment in business operations in Iceland the year before. It shall include information on the government's measures to increase foreign investment in Iceland, on foreign investment and total investment by industry and on the application of security provisions pursuant to Art. Paragraph 2 and government remedies according to Article 5.[...]" (Act on Investment by Non-residents in Business Enterprises (34/1991), last amended 24 December 2019, Article 12 [google translation])
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"Article 137: Foreign public limited companies and companies in the corresponding legal form domiciled [in a state in the European Economic Area, a member state of the European Free Trade Association or the Faroe Islands], can conduct business by operating a branch in this country.
Other foreign public limited companies and companies in the corresponding legal form may engage in the operation of a branch in this country if it is permitted in an international agreement to which Iceland is a party or the Minister deems it appropriate to authorize such. The Minister may set rules on these matters. [...]" (Act on Public Limited Companies (2/1995), last amended 4 June 2020, Article 137 [google translation])
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"Article 111: Foreign private limited companies and companies in the corresponding legal form, having their domicile and venue in [States of the European Economic Area, Member States of the Treaty establishing the European Free Trade Association or the Faroe Islands], can conduct business by operating a branch in this country.
Other foreign private limited companies and companies in a corresponding legal form may engage in the operation of a branch in this country if it is permitted in an international agreement to which Iceland is a party or the Minister deems it appropriate to authorize such. The Minister may set rules on these matters.[...]" (Act on Private Limited Companies (138/1994), last amended 28 June 2019, Article 111 [google translation])
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"ICELAND
A. Exceptions at national level
I. Investment by established foreign-controlled enterprises
Trans-sectoral: Foreign investment is accepted under reciprocity conditions. Transactions may be blocked if foreign investment is deemed to "seriously reduce competition" or to have an "undesirable effect on the Icelandic Economy". 
Trans-sectoral: Investment by foreign states or state-owned enterprises is prohibited unless an authorisation is granted.[...]" (OECD, National Treatment for Foreign-Controlled Enterprises)
Act on Investment by Non-residents in Business Enterprises (34/1991), last amended 24 December 2019, Article 12
Act on Public Limited Companies (2/1995), last amended 4 June 2020, Article 137
Act on Private Limited Companies (138/1994), last amended 28 June 2019, Article 111
OECD, National Treatment for Foreign-Controlled Enterprises
[<a href="https://www.althingi.is/lagas/nuna/1991034.html">Act</a>],[<a href="https://www.althingi.is/lagas/nuna/1995002.html">Act</a>],[<a href="https://www.althingi.is/lagas/nuna/1994138.html">Act</a>],[<a href="https://www.oecd.org/investment/investment-policy/nationaltreatmentinstrument.htm#:~:text=%22National%20Treatment%22%20is%20the%20commitment,domestic%20enterprises%20in%20like%20situations.">NTI</a>]