Foreign investment in the cultivation of rice and barley is not permitted.
"Article 4 (Liberalization, etc. of Foreign Investment)   
(1) Except as otherwise prescribed by the Acts of the Republic of Korea, a foreigner may engage in, without restraint, various activities of foreign investment in the Republic of Korea.
(2) No foreigner shall be restricted from making any foreign investment prescribed in this Act, except in the following circumstances:
1. Where he or she threatens national security and public order;
2. Where he or she has harmful effects on public health and sanitation or environmental preservation or is against Korean morals and customs;
3. Where he or she violates any Act or statutes of the Republic of Korea.
(3) The categories of businesses in which foreign investment is restricted in accordance with any of the subparagraphs of paragraph (2) and the details of restrictions shall be prescribed by Presidential Decree. [...]" (Foreign Investment Promotion Act (No. 5559 of 1998), last amended by Act No. 17799 of 2020, Article 4 [unofficial translation])
---------------------
"Article 5 (Types of Business Restricted by Foreign Investment) 
(1) In accordance with Article 5 (1) 1 of the Decree, the types of businesses subject to restrictions on foreign investment announced by the Minister of Trade, Industry and Energy in consultation with the competent minister are as shown in Attached Table 2.
(2) When a foreign investor invests in a business that has permissible standards among the industries listed in Attached Table 2, foreign investment may be made within the permissible standard.
[...]
[Appendix 2] Categories of Business with Restrictive Foreign Investment and Criteria for Permission (pursuant to Article 5)
Classification | Type of Business | Criteria for Permission [...]
01110 | Grains and other food crop growing business | Permitted, except for cultivation of rice and barley[...]" (Regulations on Foreign Investment (Ministry of Commerce, Industry and Energy Notice No. 1999-58 of 1999), last amended by Notice No. 2021-106 of 2021, Article 5 and attached Table 2 [google translation / unofficial translation of Table 2, source: Kotra])
Foreign Investment Promotion Act (No. 5559 of 1998), last amended by Act No. 17799 of 2020, Article 4
Regulations on Foreign Investment (Ministry of Commerce, Industry and Energy Notice No. 1999-58 of 1999), last amended by Notice No. 2021-106 of 2021, Article 5 and attached Table 2
[<a href="https://www.law.go.kr/LSW/lsInfoP.do?nwJoYnInfo=Y&ancNo=16131&chrClsCd=010202&efYd=20190401&lsiSeq=206503&efGubun=Y&ancYd=20181231#0000">Act</a>],[<a href="https://elaw.klri.re.kr/eng_service/lawView.do?hseq=44627&lang=ENG">Act_Eng</a>],[<a href="https://www.law.go.kr/LSW/admRulLsInfoP.do?chrClsCd=&admRulSeq=2100000136409#AJAX">Reg</a>],[<a href="http://openknowledge.kotra.or.kr/handle/2014.oak/23472">Other</a>]