Voltage Divider with low noise?
You can calculate the actual noise of the circuit, as it is basically just an 800Ω resistor in series with the equivalent source (a bit higher, as the signal generator surely has a 50Ω output impedance). At ambient temperature and 1kHz bandwidth, you would have less than 0.2µV of RMS voltage noise due to that circuit (visually &lt;0.6µV p-p). So that is unlikely to be the actual source of your noise.

The possible sources:


An oscilloscope is normally not designed to work at inputs &lt;10mV. 
Grounding problems. Noise being injected between your oscilloscope ground and circuit ground.
External interference. Signals coupling into your circuit.


How to solve it:


To actually measure your signal, you would probably have to add a small amplifier (e.g., an instrumentation amplifier that allows you to do a differential measurement).
Make sure you reduced the measurement bandwidth of the oscilloscope. 
Adding a filter capacitor would help, and you probably should add it anyway.