The answer is YES! Muscle soreness after exercise is called DOMS (delayed onset muscle soreness). This happens when you exercise a muscle that has not been used stressfully in awhile. The soreness results from tearing and or stress on the muscle fibers and as the body repairs these small tears your muscles become stronger. After exercise, you will normally feel muscle soreness anywhere from 24 to 72 hours after the activity. The intensity of the muscle soreness you experience will depend on how intense your workout was and if that muscle group has experienced a workout before of this variety/intensity.
If your symptoms of muscle soreness linger longer than 72 hours and either get worse or stay the same, then you want to consult with a medical professional. The reason for this is your exercise possibly caused a muscle strain, ligamentous sprain, or injury.