According to the Outdoor Adventures Network, it is possible for fish to drown. Fish drown when exposed only to air in the same way humans drown from exposure only to water.
Fish breathe through their gills, which regulate the amount of life-sustaining oxygen they take in from the water. When fish are removed from water, they are unable to regulate the amount of oxygen intake and instead take in lethal doses of oxygen.
Fish may also drown in water that does not contain enough oxygen, as there is a necessary balance required in water for their gills to function properly.