Yes, one of the requirements to obtain the long term residency in Poland (karta stałego pobytu) is to have a health insurance.
A long-term EU-resident permit may be granted to a foreigner who:
- has been staying in Poland legally and uninterruptedly for at least 5 years (what is an uninterrupted stay?);
- has maintained a stable and regular source of income (what is the stable income condition ->?) for the 3 years of their stay in Poland immediately preceding the submission of the application (in the case of Blue Card holders (what is a Blue Card ->?) a 2-year period of stable income is required);
- has health insurance (documents confirming the possession of health insurance ->);
- has a place of residence in Poland; [...]
Regarding which insurance to choose, check this thread:
https://polishforums.com/life/poland-health-insurance-suggestions-58444/