Yoga for tennis elbow can help allieviate this painful condition, as long as care is taken not to further strain the elbow.
Causes of Tennis Elbow

Tennis elbow is typically brought on by repetitive motion, overuse, or a direct injury. Symptoms often include inflammation and pain. Practicing yoga is nearly ideal for helping people heal from this condition because any pose other than weight-bearing ones involving the arms can be done.

Guard Your Elbows

If you find yourself in a yoga pose that puts weight on the arms, such as Table Pose, take care that you don't let your elbow creases face forward and hyperextend. Hyperextending makes the joints less stable so the ligaments may be overstretched, causing further injury.

Yoga for Tennis Elbow

Some yoga poses that will strengthen your body without causing pain and straining your tennis elbow.

Warrior II
Warrior II allows you to extend your arms fully without pain and the aggravation of tennis elbow. The sequence of the pose is as follows:

Stand in Tadasana (Mountain Pose).
On an exhalation, step or jump your feet three-or-four feet apart.
Raise your arms parallel to the floor and reach them out to the sides, keeping your shoulder blades wide and your palms down.
Turn your right foot slightly to the right and your left foot 90 degrees to the left.
Align the left heel with the right heel, firm your thighs and turn the left thigh outward so the center of the left knee cap and the center of your left ankle are aligned.
Exhale, and then bend your left knee over your left ankle, keeping the shin perpendicular to the floor.
Bring the left thigh parallel to the floor, straighten the right leg, and press the outer right heel into the floor.
Keeping the arms parallel to the floor, stretch them away from the shoulder blades, but don't lean your torso over your left thigh.
Press the tailbone slightly toward the pubis, turn your head toward the left and gaze out over the fingers.
Hold for 30 seconds to one minute, then inhale to release the pose, reverse the feet, and repeat on the other side.
Revolved Chair Pose
Revolved Chair Pose will strengthen your back, chest, thighs, and glutes, and stretch your hips.

Begin in Tadasana, arms down by your sides, sternum lifted.
Squat deeply with your weight back onto your heels, squeezing your inner thighs together.
Stretch your arms overhead, placing palms together.
Keeping your palms together, inhale and bring your arms down to the middle of your chest in Prayer Pose.
On an exhale, twist your torso to the right. This will place your left elbow at the outside of your right knee. Keep your arms in Prayer Pose.
Inhale, then exhale while deepening the twist.
Turn your eyes upward and hold the pose for three-to-five breaths.
Slowly unwind your upper body to face forward as you exhale.
Straighten your legs, bring your palms back to Prayer Position, and return to Tadasana.
Repeat on the other side.
The regular practice of yoga not only helps heal tennis elbow, it also stretches the tendons and ligaments and helps keep them flexible, significantly reducing the risk of getting tennis elbow at all.