The Panamanian-flagged Ushuaia with 89 passengers and 33 Argentine crew members sent out an alarm around midday after it suffered two cracks and started leaking fuel and taking on water, the Navy said in a statement.
Adm. Daniel Alberto Martin told local television station Todo Noticias that the passengers were of "various nationalities" and all were in good health. Another passenger ship in the area was helping the Ushuaia, which is named after the Tierra del Fuego port where the ship is based.
A Chilean Navy ship was on its way to help the Ushuaia and rescue its passengers. It was expected to arrive Friday morning.
"The ship is stable for the moment. No one has suffered any injuries and the situation on board is under control," the ship's captain, Jorge Aldegueri, told Todo Noticias. He declined to confirm the cause of the accident pending an investigation.
The ship was stuck near Wilhelmina Bay, on the western side of the Antarctic Peninsula.
The Navy statement said the cruise ship "had run aground" but was in no danger of sinking.
It is not the first cruise ship to have trouble recently in the Antarctica, which has seen a surge in tourist visits.
In December 2007, the Norwegian MS Fram carrying some 300 people lost engine power during an electrical outage and struck a glacier, smashing a lifeboat but causing no injuries.