Oklahoma lies in the Great Plains, which unfortunately means: no caves.
Karst implies subterranean drainage, which is rather rare in large plains.
Most of the state is covered by rather young sediments.
But there are two noteworthy exceptions:
A small piece of the Ozark Mountains at the border to Arkansas and Missouri in the northeast consists of limestone layers.
Here are many caves known, but none is open to the public on the Oklahoma side of the border.
The gypsum layers of the Permian Blaine Formation.
A small area of gypsum outcrop in the northwest form a small area of gypsum karst.
The only gypsum cave in the United States, which is open to the public, can be found here.