Can you treat a sprained arch of the foot?

Yes. May have strained the plantar facial ligament. The usual treatment is to decrease inflammation and improve foot function. Try good shoes and support at all times, ice with frozen water bottle under the arch, antiinflammatories as tolerated and limit weight bearing activity. If persists, see your foot specialists. Dr l.
Yes. Sprains in various joints are usually treated similarly. For the foot arch, some rest is important, so one should avoid over-using the foot until it improves. Cold packs can help decrease inflammation. Some people roll an ice-cold can of soda back and forth with the bottom of the foot. Anti-inflammatories (motrin) can be taken a few days. Adding an insole such as superfeet will support the arch.