What is the normal recovery time for ligament injuries to heal?

A few weeks. Ligament injuries heal slower than muscle problems because there is less of a blood supply to the ligament itself. After the acute injury heat applied to the area will improve blood flow and speed healing. Once the initial pain and swelling goes down gentle motion also stimulates healing.
Ligament injuries . Heal in 6-8 weeks just like bone or soft tissue but location degree of injury associated issues and pre existing status of a joint all play a role, by healing what one means i'd the tissue is structurally better. But symptoms may persist for a long time depending on many factors mentioned . So it may take a lot longer to feel better or feel healed.
Ligament. Depends upon location & severity: partial or complete. May take a few days for a mild ankle, wrist, or elbow sprain. May require surgery for complete acl tear.