Amplified electret mic gives a lot of low frequency noise
Low frequency noise (~50/60Hz) is mostly caused due to induction of electrical noise into the traces on PCB (or wires, if you're not using a PCB). This is particularly bad with breadboard setups due to the nature of their construction. 

Since you have figured out that the source of noise inductance is between your microphone and the amplifier, you could try a few techniques to reduce it:


Use shorter wires between mic and amp
Use electromagnetically shielded cable (wrap some grounded aluminium foil around it maybe?)
Use a twisted pair cable (keep them differential)
Keep the ground connection of mic close to that of amp, and use equal
length wires (adds to the above point)