A rescue vessel is heading to the area to assist the Explorer, which was listing at 25 degrees and taking in water.
Passengers pay about $8,000 per cabin to travel on the cruiseliner, which makes two-week cruises around the Antarctic.
The South Shetland Islands lie about 120km north of the Antarctic Peninsula and has been part of the British Antarctic Territory since 1962, although they are also claimed by Argentina and Chile
Rescue centres in Virginia in the US and Ushuiia in Argentina are co-ordinating rescue efforts.
Source: News Agencies