Yes, a foreigner can register as an individual entrepreneur and all business activities on the territory of Ukraine.
According to Article 4 of the Law of Ukraine "On the Legal Status of Foreigners and Stateless Persons", foreigners who are legally present on the territory of Ukraine have the right to carry out entrepreneurial activities, for which it is now not necessary to obtain a temporary residence permit, on the contrary, FOP registration is the basis for issuing a permit.