Does this photodiode need an operational amplifier?
Generally speaking, you can consider the following:

A transimpedance amplifier (using an opamp) is used for


Higher speeds - If the photodiode has a significant capacitance.
Higher amplification - You may get into trouble with biasing otherwise.
Better linearity - The photodiode biasing voltage is more constant.
Low output impedance - The opamp also acts as a buffer.


Just the regular resistor biasing can be used for


Lowest power consumption - Only a single branch with current (usually negligible).
Lower noise - No added noise by the opamp + possible compensation capacitor.
Simplicity - No need to look at stability or choosing a suitable opamp.


My advice is to keep a transimpedance amplifier in mind. When used correctly it almost always leads to a better performance. If you're designing a PCB for example, you can always choose not to mount the opamp if it is not necessary.