The woman, whose identity was not disclosed, was holidaying on the Sea Spirit cruise ship and had boarded the dinghy to approach a fjord, when it was suddenly hit by a large wave.
The 13 people on board were thrown overboard in the glacial waters before being washed ashore by the waves. The woman died in the accident, though the exact cause of death was not known.
Three other people were lightly injured, the office of the governor of Svalbard said in a statement.
Tourism is one of the pillars of Svalbard's economy, along with scientific research and mining. Spitsberg is the largest island in the archipelago, which is located about 1,000 kilometres (620 miles) from the North Pole.