Zoysia is a warm season lawn grass that can be a weed in a cool season grass lawn such as Kentucky bluegrass or fescue. It can be difficult to control. Small areas or patches of Zoysia in a lawn can be treated with a non- selective type herbicide such as roundup, kleenup or finale. A nonselective herbicide can potentially kill any plant that it comes in contact with. So be careful when spraying around plants you want to keep!
For best control apply herbicide when the Zoysia plants are fully green, actively growing and not under drought stress. Often plants will regrow so more than one application will probably be needed. You should realize that area treated will be brown and unsightly until you get all of the Zoysia controlled. You can reseed the area five to seven days following the final herbicide application. Be sure to read and follow the label directions.