Opamp current source stable in simulation but unstable on prototype
The problem is the loop has not been compensated correctly, it wants to oscillate as shown your graph on the red scope trace (the voltage probe) I have a similar plot below:



This can also be seen in the closed loop gain (green trace) the hill at 10Mhz indicates that there is a Q point that wants to ring around 10Mhz (but why not 1Mhz like the design resonates at? stay tuned). 

So how to fix this? Use a lot more capacitance, 10uF and move it to the other side of the resistor. After doing so you get the red trace, which shows very little ringing.



There are a few other caveats, there has been no parasitics simulated! So either build your design as close as possible to the schematic OR simulate the parasitics by estimating them from the board. Part of the reason for the simulation showing a resonance point at 10Mhz and the design at 1Mhz is parasitic inductance has not been simulated. 

Cables will contribute 10nH's, the traces can also have some inductance and resistance. I could go into much detail but have ran out of time. The way to calculate this is with trace inductance/resistance calculators.

In these kind of circuits inductance can change things, where it normally can be neglected. You may also want to  include the source resistance of the wire and the simulation as the current source and the power filter caps can also contribute to resonance.