Driving conditions in the county have been described as treacherous with flood waters affecting many roads.
Gardaí are warning motorists to take extreme caution on the roads.
They say conditions are expected to remain poor right through the morning, with extra caution needed.
A wind gust close to 90km/hr was recorded at the Met Eireann station at Finner just after midnight as the storm took hold, with gusts increasing throughout the night.
Coastal areas of Donegal are getting the worst of the weather.
The Irish Coast Guard has issued a warning to people driving or living along the coast.
“The morning should see highest wave heights off the Donegal of up to 7 or 8 meters,” said a spokesman.
“Thankfully the height of the storm does not coincide with high water. However coastal areas, cliffs and piers may still be very dangerous. Please exercise caution and use common sense – the next breaking wave may be much bigger and could just be the one that sweeps you away.”
Gonzalo lost its tropical storm status yesterday and is now classed as an ‘extra-tropical’ depression.