How long does it typically take a leg muscle injury to heal?

4-6 weeks. Most muscle injuries will heal in 4-6 weeks. During that time care should be taken to avoid re-injury. After a few weeks gentle stretching is advisable to avoid re-injury.
Recovery. The recovery for an injury varies by patient, severity, desired level of activity, and the specific muscle that has been injured. Rest ice compression elevation for the injury will aid in the recovery process. If you fail to improve, seeing an orthopaedic specialist may be required.