Why ammeter use fuses and volt meter do not?

An ammeter measures current THROUGH a circuit, a voltmeter measures current ACROSS a circuit.

The ammeter is connected to a power source in series, essentially actually becoming part of the circuit. The current is flowing directly through the ammeter as if there were a wire in its place. If there is a surge from a substantial power source, the ammeter would be destroyed and the user could be severely injured.

The fuse will "blow" if its "load" is exceeded breaking the circuit.

A volt meter is connected to a power source in parallel because it has an extremely high resistance and little to no current would get through. You don't need a fuse because the current doesn't flow through it openly.