Homeowner Sue Abel said she "heard a crack on the other side of the house" at about 00:30 BST on Monday.
The stable - which was empty - had travelled about 50m (164ft) from a neighbouring field, Mrs Abel said.
She told the BBC: "I've never known the winds, in the 10 years I've been here, [to be] at that strength."
Emergency services arrived promptly but the stable was left in place on Monday because the winds were "still quite brisk", she added.
The front of the property suffered some damage, including a number of smashed windows.
Storm Katie disruption round-up
Your pictures of Storm Katie
Storm Katie - the 11th named storm of the winter - caused considerable disruption across England, south Wales and the Channel Islands on Monday.
Gusts of up to 106mph were recorded at The Needles off the Isle of Wight as the storm hit the south of England.

The 20-year-old Wales Under-19 international had a recent loan spell at Stevenage, but did not make a first-team appearance.
Crowe, who has yet to play for Ipswich, has been signed after Will Norris returned to Cambridge United.
Braintree are due to face Kidderminster at home on Tuesday after their weekend game at Torquay was postponed.

Earlier, the government announced 21 locations for enterprise zones in England in an effort to boost economic growth.
Gloucestershire's bid focused on Gloucester and Cinderford.
But Communities Minister Bob Neill said the county could still benefit from other job-creating projects.
"It's no disgrace to Gloucestershire at all, they did hard work, I know that," he said.
"And what I'd say to them is do not be discouraged.
"We are working with local enterprise partnerships and local councils beyond the enterprise zone projects, for example giving councils the ability to discount business rates to attract businesses into the area, giving the ability to set up simplified planning regimes."
Plans for 21 nationwide zones were first set out in March's Budget.
Zones have been confirmed for sites in Cheshire, Cornwall, Gosport, Norfolk, Hereford, Kent and Oxfordshire.
Other locations include Essex, Suffolk, Northampton, Leicestershire, Cambridgeshire and the Humber Estuary.
Ministers said 30,000 new jobs would be created by 2015 by giving cheaper business rates, super-fast broadband and lower levels of planning control.
An entire stable was lifted by a gust of wind and dumped into the front of a house in Alderney as Storm Katie lashed the Channel Islands.
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Ipswich Town goalkeeper Michael Crowe has joined National League side Braintree Town on a one-month loan.
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Gloucestershire's failure to secure an "enterprise zone" for the county is not a reflection on local businesses, the government has said.