Anterior Compartment Syndrome. Go see someone who does biomechanics analysis -- who will videotape you walking and running on a treadmill with and without shoes. They will be able to point out what you're doing to aggravate the muscle and give you a solution.
I had this, and was told that I was holding my feet flexed upwards constantly while running and walking, which lead to the compartment syndrome through overuse. Try flexing your foot upwards, and you'll see that the muscle you're speaking off will tighten.
I had to relearn how to run so that I gave the muscle in question a break. A proprioceptive cue I used is to drag your toes while walking. It helped me learn how to relax that muscle for a brief moment while my foot is in the air while walking/running. After 2 weeks of obsessively practicing this, I found relief. Got better and better over the next few years. Bothers me now only after a road race, particularly with downhills. Also flares up when I'm overtraining, so a good warning sign for me actually. Never had to have surgery.
Doctors may tell you to get surgery -- a fasciotomy (I don't know how to spell it). This entails cutting holes in the muscle compartment to relieve pressure. Mary Slaney had this done a few times. It can help, but not a permanent solution, especially if you are overusing that muscle because of the way you run. You'll just have to do it over and over if you don't correct the biomechanical problem. Surgery should always be a last resort anyway.
Another tip -- if you wear loose-fitting flip-flops or sandals, it can aggravate it. If your shoes are about to fall off your feet, you will subconsciously hold your feet flexed up and rigid to keep the shoes on -- which directly uses that muscle. Wear shoes that fit snuggly enough that you can move your feet around in the air and they don't fall off.