The ship ran aground on a sandbar on Sunday morning about 38 kilometres from the Latvian coast. None of the 651 German passengers or 320 crew were hurt.
"Two coast guard ships have already arrived with plans to pick up the passengers," Herbert Fervers, executive director of the German tour operator Lord Nelson Seereisen, told German news agency DPA on Monday.
Fervers, who is on board the 200-metre cruise ship, said four tugboats had been unable to free the Mona Lisa. Divers inspected the hull of the ship and found it sustained only minor damage.
"It was a steering error. The ship did not keep its course," Fervers said, adding that the Greek officer steering the ship at the time of the crash was experienced and was not under the influence of alcohol.
This is the ninth time the ship has run aground in its 42-year history, Latvian Defence Minister Vinets Veldre told reporters, according to DPA.
Vacationers paid an average of €1,400 ($2,165) for a 10-day cruise that started on May 1 in the northern German city of Kiel and was to have continued over Riga, Tallinn, St. Petersburg and Helsinki. They will be evacuated to the Latvian port of Ventspils and brought by train to Riga, then flown back to Germany on Tuesday, Fervers said.
"Though the passengers are sad the trip had to end early, they have been quite understanding," he said.