There have been several reports of damage, with trees and fences blown down in the early hours.
A fence bordering the car park at the McDonald’s branch in Sunningdale Road, Balby crashed into the car park, narrowly avoiding a number of parked cars.
A yellow weather warning for wind has been issued for northern England, including Doncaster and South Yorkshire for Sunday and into Monday.
Alerts are also in place across Scotland, Northern Ireland and northern England for most of Saturday.
Named by the Danish Meteorological Institute, Storm Malik is expected to bring winds of 60mph and up to 80mph in coastal areas, on its way towards Denmark, with lower speeds inland.
The Met Office said Storm Malik's impact would be greatest in Denmark on Sunday but the UK would be "dealt a glancing blow" from Saturday as it moves eastwards.
Rail services between Doncaster and Scotland on the East Coast Main Line could be impacted by the weather with passengers advised to check on services ahead of travel, particularly on services north of Newcastle.
The yellow warning of wind is in force from 6pm on Sunday to noon on Monday.
A spokesman for the Met Office said: “Strong winds will likely cause some travel disruption and generate some large and dangerous waves around the coasts.
“Road, rail, air and ferry services may be affected, with longer journey times and cancellations possible.
“Some roads and bridges may close and power cuts may occur, with the potential to affect other services, such as mobile phone coverage.”