It issued a yellow warning of wind, saying gusts of up to 75mph (120kmph) could occur locally, particularly to the west of the mountains.
It added the unusual easterly direction could add to the impact of the winds.
Forecasters said disruption to travel on roads and at sea was likely.
The affected counties are Conwy, Anglesey, Gwynedd, Pembrokeshire, Carmarthenshire, Ceredigion and Powys.
Gusts overnight brought a tree down in Menai Bridge on Anglesey, closing one of the main routes into the town.
The council said Telford Road was expected to remain closed for most of Monday to allow clean-up work to be carried out.
The Met Office has warned of very strong winds along the western coastlines of Wales throughout the day on Monday.