Two people were arrested as part of the operation on Sunday in the seaside town of Cangas near the border with Portugal, a police spokesperson said.
The submarine was "likely" transporting "several tonnes (of cocaine) but this is just an estimate", a source close to the investigation said.
Spanish media said the submarine was carrying over three tonnes of cocaine from Colombia.
The submarine, about 20 metres (65 feet) long, came from South America, another source close to the investigation said, without specifying which country the vessel departed from.
"It is not the first time but we don't see this every day" in Europe, the source added.
Drug traffickers, especially from Colombia, have been caught using submarines to transport cocaine into Mexico, and from there into the United States.
In September the US Coast Guard, with the aid of the Colombian navy, intercepted a submarine carrying over five tonnes of cocaine off the coast of South America.
Galicia, one of the country's poorest regions, is a top entry point for cocaine into Europe. A maze of coves, caves and inlets dot its rugged coastline, making it a smuggler's paradise.
Spain accounted for the second-highest proportion of cocaine seizures in the European Union last year after Belgium, with 41 tonnes apprehended.
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