The time it takes for a sprained ankle to heal depends on the severity, or how badly the ligaments were stretched or torn. Mild ankle sprains usually take about 1-2 weeks before it completely heals, while it is 4-6 weeks for moderate, and 8-12 weeks for the severe ones. Following the RICE (Rest, Ice, Compression, Elevation) technique usually leads to a faster recovery time.
The recovery time for an ankle sprain depends on the severity of injury. But generally, the range of motion, flexibility, and strength of a sprained ankle is expected to improve within 1-2 weeks. However, it might take up to several months to regain the same level of function before the injury occurred. To read more about ankle sprains, you can visit this site: http://orthoinfo.aaos.org/topic.cfm?topic=a00150#Rehabilitation