Bizarre Behavior in a Phototransducer Amplifier
You need a negative supply on the op-amp (say +/-2.5V) for this to work. 

The op-amp output has to swing negative to supply current to equal the PD current. It cannot possibly swing below ground without a negative supply, in fact it may only be able to get within some tens of mV of ground depending on load connection etc. 

Optionally (and probably better for this application) you could flip the PD around, but you still may get a bit of a dead zone near zero because the output can't get quite to zero. 

If you intend eventually on connecting it to an ADC input on the Arduino you will want to swap the PD around and perhaps to bias it above ground a bit, then you can stay with the 5V supply and within the range of the Arduino ADC. 

If you don't need to go right to zero for very low light levels, just flip the PD.