The amber warning will be in force from 9am tomorrow until midnight, with another yellow warning in place for the far north of Scotland between midnight and 9am on Monday.
Gusts of up to 80mph could arrive north of the border, the agency said, with a "small chance" of danger to life from flying debris and large waves on the coast.
It added that some roads and bridges could close, with the possibility of cancellations affecting trains and flights, as well as potential damage to buildings.
Transport Scotland warned of likely disruptions to public transport, including the country's ferry network.
A statement said: "A windy period is expected across the whole of the UK on Sunday and into Monday, but across parts of Scotland, Northern Ireland, northwest England and northwest Wales there is an increased chance of some disruption.
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