The warning states the winds could cause severe damage to buildings, with roof tiles possibly being knocked loose, with the possible closure of some roads and bridges.
Transportation services may also be affected, with longer journey times and cancellations a possibility.
The Met Office said of the warning: “Gusts of 55-60 mph are expected widely around south and west facing coasts, but possibly also briefly inland.
“There is a chance that a few exposed places could see gusts near 70 mph.
"Strong gusts associated with blustery wintry showers will follow from the north.
"A swathe of very strong winds will reach Northern Ireland later Sunday evening in association with Storm Franklin.
"These very strong winds will spread to many other western, central and southern areas of the UK overnight and early Monday, with gusts widely 50-60 mph, whilst west facing coastal districts will see gusts of 65-75 mph.
"Winds will ease steadily from the northwest during the remainder of Monday.”