Ligament problems are not listed among the side effects of Celebrex. That does not necessarily mean that Celebrex doesn't cause ligament problems. It just means that it has not been reported to cause the problems at this time. What Celebrex can cause and commonly causes is side effects like constipation, diarrhea, headache, heartburn sore throat, and some other side effects like allergic reactions and swelling of the mouth or face, tightness in chest, fainting, dark urine, red, blistered, swollen or peeling skin. If any of the side effects get too severe, you should contact your doctor and let him know what you are going through.