Storm Ali brought gusts of more than 90 miles (145 kilometres) an hour and intense rainstorms.
Officials said the woman died in her sleep when her caravan was swept off a cliff in the west of Ireland.
"At approximately 7.45am, a report was received that a caravan had blown off the cliff at the above location. A search was carried out at the scene on the beach and after a short time the body of a female in her 50s was recovered," Irish police said in a statement.
They did not confirm the identity of the woman.
The Swiss foreign affairs ministry confirmed to The Local that a Swiss woman had died in Ireland and said Swiss consular staff were in contact with the woman's families.
Consular staff in London were in contact with Irish authorities, the ministry said.
In another fatality, a falling tree killed a local man in Northern Ireland.
The UK's national weather service said the first named storm of the season should partially subside overnight.
"Unsettled" weather was forecast through the weekend.