I would assume the spikes are occurring with each step of the motor. Is this the case? If so, then you can't eliminate the spikes, you can only mitigate them.
The motor is an inductive load, so the current cannot stop instantaneously when one of the switches (which I assume are mosfets) open. That motor current has to go somewhere, and that is what the free-wheeling diodes are for. But the free-wheeling diodes cannot turn-on instantaneously, so the voltage will rise until the diodes start to conduct and give the motor current a path to flow. That's what those spikes are.
There are several ways to mitigate the issue, but the most common way is to use faster free-wheeling diodes. The specification that you need to look for is "reverse recovery time". If your bridge is using the mosfet body-diodes for free-wheeling, than faster diodes may be in order, as the body-diodes are not necessarily fast.
Another way to mitigate the problem is to slow-down the turn-off of the switch. The slower turn-off allows more time for the free-wheeling diode to start conducting. But it may not be as simple as that sounds, as a longer turn-off could cause shoot-through if you don't compensate with the turn-on of the other switch in that half-bridge. Softening turn-off is also how you would reduce EMI, but at the cost of greater heat dissipation in the switch.
If you only want to mitigate the over-voltage to the power-supply (the spikes not being a problem to the bridge), a fast zener at the input of the bridge may be all you need. A high-frequency capacitor might also do the trick.
--- Later ---
I just looked at the schematic, and realized that all of the components I mentioned earlier are buried inside the chip, and not accessible to you. So the fast zener or capacitor approach is all that's available. The board already has a pair of 0.1uF ceramic caps (c2 and c3), so I would suggest a zener (around 30 volts) across VMOT and GND.