The 114-foot Draken Harald Hårfagre had been making its way across the North Sea having set off from Haugesund in Norway.
Captain Björn Ahlander said the longship had been making good progress towards Orkney when a big wave hit, causing the mast to break and go overboard.
Nobody was hurt.
"We had been out for three days, everything went smooth and fine and the ship was sailing good," he said.
"Suddenly a big wave struck, in combination with the wind pressure, the mast went off very quickly and overboard."
The ship contacted Shetland Coastguard, but no assistance was required.
The ship changed course for Lerwick and, using its engine, arrived on Saturday.
In addition to visiting Shetland and Orkney, the ship had been planning to visit Dublin, Liverpool and the Isle of Man this summer.
The Draken Harald Haragre is named after King Harald Fairhair, the first Norwegian king, who reigned between 872 and 930.