Mountainous areas, particularly in the north of the popular holiday destination, were particularly affected by the passage of Storm Juliette, with roads blocked in some areas.
Over a metre (three feet) of snow has accumulated on some parts of the island's northern Serra de Tramuntana mountain range since the storm hit on Monday, according to national weather office AEMET.
The regional government of the Balearic Islands said it was working with security forces to reach a mountain road and two shelters "to rescue people who are still isolated" there.
All of the people are in "good health", it said in a statement, adding three helicopters were taking part in the "search and evacuation" operation.
Spanish army's emergency unit UME said around 90 of its members, backed by snowploughs, were helping to clear roads.
Rescue crews were able to clear a path to the 13th-century Santuari de Lluc monastery, where around 100 people were trapped by the snow, local emergency services said.
"Twenty people were evacuated. The rest will stay in the monastery," it added in a message late on Tuesday.
Located in the Serra de Tramuntana mountain range, the monastery is a popular starting point for walking tours.
Local emergency services urged people not to come to the mountain to look at the snow, "either by car or on foot".
"Let's work together to support the operation to rescue people who are still trapped," the emergency services requested," it added in a tweet.
Known for its picturesque beaches, Mallorca -- part of the Balearic Islands which include Ibiza -- gets more than 300 days of sunshine per year, according to its tourism board.
While heavy rainfall is common in the autumn and winter, heavy snowfall is rare.
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