I assume that you have a water shut-off valve at the water meter that supplies your house. This meter is usually located out on the sidewalk in a cement box. If you feel comfortable doing so, you can shut off this valve at the meter, and work on the valve in your basement. Your best bet would be to remove the defective basement valve and install a new one.
FYI, the municipal water company is responsible for any plumbing lines/fittings up to your water meter. You are responsible for the plumbing between the meter and your house. Unless you feel real confident to replace the basement valve yourself, I’d suggest hiring a plumber. It is an easy job, and shouldn’t cost much. Such a job shouldn’t take more than 1-2 hours.
NtP