Can an injury from sports give you brown urine?

Sign of OverTraining: Exertional rhabdomyolysis - is a rare, but serious complication of too much exercise. It can affect people of any race, age, or fitness level. When it occurs after exercise, it doesn't always require the exercise session to be extreme. It appears that the key factor in many cases is an abrupt increase in the intensity of exercise. The other cause could be delayed-onset muscle soreness (doms).

Yes: The brown urine is probably blood and you should see a doctor to determine where the bleeding is coming from.