Reducing Transimpedance Amplifier Noise
Is this standard behavior for a TIA?


Yes, unfortunately it is and no, your cable isn't acting as an antenna but as a capacitor. The cable capacitance is connected from -Vin to ground and this makes the non-inverting gain of your amplifier very large at high frequencies.

What has non-inverting gain got to do with a TIA I hear you ask possibly?

Well, in series with +Vin you have a noise source and this is the equivalent input noise source of your amplifier (op-amp) and, with zero capacitance on -Vin you have a non-inverting gain of unity.

Now add some capacitance and the non-inverting gain becomes: -

$$1+\dfrac{Rf}{X_C}$$

Clearly, as you add more capacitance, Xc gets smaller and the "noise gain" (yes, that's what it is called) gets bigger.


  What can be done, if anything, to reduce this kind of noise?


Most folk add a feedback capacitor across Rf to counter the capacitance on -Vin. See also this answer for more detail as pertains to a photodiode amplifier using a TIA.