Ministry of Education controls the money and conducts yearly performance target negotiations bilaterally with each higher education institution. You actually need a permit from the ministry to run any kind of school. Even our few "private" primary and secondary schools are publicly funded and regulated accordingly.
Independent expert body FINHEEC audits universities quality management schemes regularly. Some European countries use accreditation-based evaluation (for single degree programs) instead of system wide audits. At least one Finnish university has also acquired ISO 9001 cert, but it was seen as more labor intensive and not providing the same benefits (benchmarking, benchlearning) as the required peer-based audits.