Before you change your whole system because of one employees abuse, you need to think it through. Do you want to lock out everyone from sending or receiving ANY non business related emails?
Do you have a written policy for personal use of email?
If not, you need to get one published because it would be difficult to repremand the employee with out it.
If you do have a policy, are you ready to enforce it with a warning, suspension, or termination?
If no, your policy is not worth much.
If yes, have the employees supervision talk with the employee and be firm about the consequences. You must be willing to follow through,