Spanish coastguards and members of the civil guard helped to get passengers to safety after the incident occurred in the port of Denia at 11.30pm on Friday.
There were 393 people and 70 vehicles on board the fast ferry.
Passengers with cars had to leave them on board but coaches were put on to Valencia or Alicante with stops en route.
The rescue operation reportedly went on until 2am on Saturday. There were no reports of any injuries.
In a statement, Balearia said: “The fast ferry Pinar del Rio ran aground at 11.30pm last night by Denia’s harbour wall without any personal injury to passengers or crew.
“The fast ferry, which was coming from Palma and Ibiza, was going to dock in the port.
“There were 393 people and 70 vehicles on board.
“All the passengers were unharmed and were evacuated using Spanish Coastguard and Civil Guard vessels and a Balearia tug.”
The statement added: “Balearia will remain in contact with passengers who still have their vehicles on board to inform them about when they can remove them.
“The company removed the other belongings they had on board and have handed them over.”
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