Op-amp inverter amplifier, low current, with AC noise at 50Hz
Reading your description one can tell you're in a country that has 50 Hz mains power.

You don't say how you're putting the circuit together, breadboarding or otherwise.  But there is no reason to have such high resistor values.  The Johnson noise will also be too high and the main issue is that your wiring is picking up stay fields and the high resistance is preventing the op-amp from being able to dominate the aggressor signal.

Further improvements you can do:


place a resistor equivalent to the parallel resistance 1M||10M from the non-inverting input to ground.
shield the inverting input to reduce the chance of pickup.