My active, fit husband fell while playing tennis because of weakness in his leg. He does exercises for his back, but has sciatica, too, now. Why?

Sciatica. Herniated disc many time does not cause symptom when it does is b/c it's touching the nerve. Bending forward is the common way to bulge the disc back toward the nerve therefore causing shooting pain below the knee. See doctor for exam.
several things. Sciatica is caused by nerve root impingement in the spinal canal. This can be caused by disc bulges, neuroforaminal narrowing, facet arthropathy, and several other things. If he also has weakness, he should seek urgent medical evaluation.
Pinched Nerve/Muscle. Most times back pain that is sudden onset will resolve. He should use anti-inflammatory meds like ibuprofen, aleve around the clock and even tylenol (acetaminophen) to help. If this does not resolve he should see his doctor for other options as well. If it still does not resolve, i would recommend him to see a spine specialist for a full evaluation and testing. He may need to get an MRI to see inside.