The investment at the Golden Jubilee Hospital will lead to 1,500 additional operations covering joint replacements and cataracts, Alex Neil said.
"We have seen a significant increase in the number of people who need cataract and joint surgery and increasing the number of operations at the Golden Jubilee will help boards to manage these increases in demand," he said during a visit to the hospital in Clydebank, near Glasgow.
"This builds on the £72.2 million that NHS boards are already investing this year to increase their capacity, and will help ensure patients across Scotland have access to the fastest possible treatment."
The money will be in place for 2014-15 and aims to help deliver 300 joint replacements and 1,200 cataract operations each year.
The cash will be invested in recruiting additional doctors, nurses and support staff.
Jill Young, chief executive of the hospital, said: "This further expansion of the Golden Jubilee solidifies our position as the largest elective orthopaedic centre in Scotland, providing an expert role in both simple and complex conditions. We are also now one of the largest providers of ophthalmology in Scotland.
"The expansion plan means that we will carry out over 25% of all hip and knee replacements and at least 12% of all cataract operations for NHS Scotland. In reality, this means more patients will benefit from having their operations carried out by our orthopaedic and eye specialists within their treatment time guarantee."