Most visitors to Belarus are required to possess medical insurance to cover the entire period of their stay. Evidence of having purchased medical insurance with specific reference to coverage in Belarus for a minimum of €10,000 is now asked for as part of the visa application, so there's no way around this. If you have travel insurance already, ask your insurance company for a letter stating that you are covered in Belarus and for what amount. If you haven't got insurance already, you can simply buy one of the Belarus government's officially endorsed policies: check the embassy website in the country you're applying from.
Citizens of countries that have reciprocal medial agreements with Belarus, for example, the UK, do not need medical insurance to apply for a visa. Insurance is also not required for holders of transit visas.