The incident happened near a Home Bargains store in Limavady.
At the time, winds were recorded gusting between 50-60 mph at nearby Magilligan.
“I went over to offer help when I saw it, everyone was shocked but thankfully no-one was injured in the accident,” Paul McCorriston told BBC News NI.
Mr McCorriston said he spoke to the father who was travelling in the van with his two children.
“He told me he slammed on the brakes and the branch came through the driver side of the window,” said Mr McCorriston
“Any further and God only knows what could’ve happened.”
There were reports of trees coming down in other parts including in counties Antrim and Donegal.
The strongest winds on Wednesday have been recorded in Orlock Head in North Down.
The weather station recorded gusts of wind up to 70 mph.
No weather warnings had been issued ahead of the windy conditions.
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