The Verdict: Need More Info
A permit exists for this, but it follows a designated project, not the investor. Your first step is the economy ministry and the investment-promotion agency, not immigration.
Article 110(19) of the Aliens Act issues a residence-and-work permit without a labour market test to a third-country national coming to carry out a strategic investment project, or holding incentive measures under the investment-promotion law.
What makes it available is the project being designated, or incentives being granted, under those separate laws. Expect them to want scale, sector fit and a concrete plan. The Aliens Act itself sets no investment figure; any threshold sits in those laws.
If the project is smaller, the entrepreneur route is the realistic one: article 110(3) gives the same kind of permit to anyone holding at least 51 per cent of a Croatian company and working in it, with no minimum capital.