It's recommended that a microwave be on it's own circuit. Microwaves draw a lot of power.
It could be that your wiring in kitchen could be only 14 awg which can only handle up to 14 amps safely.
Most houses are now wired with 12 AWG wire which can handle up to 20 AMPS.
It's probably safe but you might want to get an electrician to look at it to make sure nothing else is wrong on the circuit.