Shaky hands after exercise is generally nothing to be worried about. Fatigue and low blood sugar are likely the culprits. However, some medications, coffee and tea and having an overactive thyroid may also be contributing to the issue. If the tremors don't resolve a few hours after your workout, or the issue is more chronic, visit a doctor to determine the cause.
Even though it may not look like it, your hands shake very, very slightly every moment you're awake. As a muscle moves, some motor units are contracting and shortening while others are relaxing and lengthening. Due to the large amount of motor units in most muscles, the overlap of contracting and relaxing motor units gives the appearance that the area is contracting smoothly overall.
After strenuous exercise, some motor units drop out of service due to fatigue. With fewer motor units working at once, the difference between the contracting and relaxing becomes more apparent. This is when you will actually begin to see the shakiness in your hands. After sufficient rest, the motor units that were fatigued will be replenished and the contractions will be smooth again, halting any visible tremors.
Low Blood Sugar
Aside from fatigue, low blood sugar may also be the culprit for shaky hands. After a workout, especially if it was long and strenuous, your body's nerves and muscles are deprived of fuel, which makes your adrenaline system kick into gear. Once you eat, the shakiness should subside. Aim for carbohydrates like oatmeal or fruit instead of sweet, sugary snacks.
Too much coffee and tea can also cause shaky hands. If possible, avoid excessive consumption, especially prior to your workout. An overactive thyroid will also cause tremors as well as certain medications for asthma and depression. If you have eaten and have rested a few hours after your workout and you are still shaking, it is time to see a doctor to rule out any other serious problems.