A Hancock County ban on smoking in public that goes into effect July 1 prompted the move by Eldorado Gaming Inc.
Mountaineer, which has a hotel, golf course and spa, is a popular destination for Ohioans.
The company presented its plans to the county health board on Tuesday.
The patio will have an estimated 119 slot machines and six gaming tables. It will be built in a former gaming area that is unused. Two exterior walls will be removed and replaced by a 12-foot-high fence.
Mountaineer officials had said the ban on smoking would reduce annual revenues by 17 percent, the newspaper reported. The casino is Hancock County's largest employer.