Yes. Foreigners who are on an Employment Pass, EntrePass, Dependant Pass or any other work pass can buy health insurance from a private insurance company in Singapore.
There are various types of medical insurance available that cover critical illness, long-term care, hospitalization, etc.
The health insurance premium will vary depending upon factors such as your age, current medical condition, your income, the type of coverage you choose, etc. Premium can range from S$75 up to S$400 a month depending upon various factors.
Usually, most insurance plans will not cover you for pre-existing conditions i.e. a long-term ailment that you are already suffering from prior to taking out the insurance policy.

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(Chief Editor:xiaoya)