The short answer is that it depends on the internal circuitry of the remote. I have a Harbor Breeze fan/light combo that came with a wireless remote, and I know that there are protective circuits inside the receiver that detect if there are non-incandescent bulbs in the system (e.g. CFLs/LEDs, which can cause power spikes, don't work with simple dimmer circuits, etc), or if the wiring is connected incorrectly. This protects against certain short-circuits and against overloading the wiring. From what I know, the basic design assumes you will either use it for a fan only, or a fan with light.
If this is the case, you can't use the remote to control just a light. The receiver will detect that the motor circuit is discontinuous and shut off to protect itself. However, the receiver may not be that "smart", so as long as the Motor Hot wire is capped off to avoid arcing, shorting and electrical fires, the circuit through the Light Hot and Motor/Common Neutral wires should still work. You just have to connect the receiver unit properly; the wires coming out of one side of the receiver should go to the J-box, matching white to white and red or black to red or black, and the wires in the other side should go to the light, again matching white to white and black or red to blue.
If this doesn't work, you're probably going to have to put the light on a wall dimmer. There are models of wall switch that are also receivers for remote controls. Lutron's "Maestro" system uses one wired wall switch, to which a number of wireless controls can be linked and communicate with it via RF. This allows for, for instance, 3-way switching where there used to be none, without having to fish wire. In your case, the Pico remote control works with a Maestro switch and allows similar functionality to what you want with the Harbor Breeze control; a remote you can take in hand and control the lights from anywhere in range of the wall switch. You can get this system at a Home Depot or online. Downside? It's toward the cutting edge of home lighting controls, and so is pretty high-end; the switch and remote control combo is about $80.
Many dimmers have an adjustment for the minimum level. You don't mention what type of dimmer you have but you can consult the instructions on how to adjust this. As @dslake mentions in his answer, adjustments might be via a knob or screw, but if it's digital, it could also be a button sequence.
Needing to perform this is more common with electronic dimmer switches since they need to work for many different types of bulbs (incandescent, CFL, LED).
Best Answer
Light dimmers use triac based phase control for dimming purpose. It chops the sine wave somewhere in between depending upon the knob position, which produces a signal like this:
(a) is pure sine wave. (b) and (c) represent modified sine wave going to the appliance depending upon dimmer knob position. This works well for dimming an incandescent bulb because they give off light based on heating of the filament.
However when you give this waveform to a ceiling fan, it won't behave very well. Most obvious issue will be a humming sound specially at a lower speed (corresponding to signal (b)). Lesser obvious issues might be increased energy loss in the coil.
Nowadays companies have started using a series capacitor to reduce the voltage while maintaining a sine wave which eliminates humming while reducing the fan speed.