Four fire crews were called to the scene in Ripon at 3.52pm yesterday to reports of people trapped in the flowing water.
They recovered two men and a dog from the Transit van.
Station Manager for Andy Creasy criticised their "reckless stupidity" after he asked them why they had attempted to cross the river.
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The men responded that their SatNav told them to go that way.
Mr Creasy, who is also the district manager for Ripon, Boroughbridge, Lofthouse & Masham, shared the incident on Twitter.
He said: "Ripon Blue Watch along with multiple FRS resources from North Yorkshire Fire and Rescue Service were mobilised along with North Yorkshire Police to this.
"I had one question only, why did you attempt this?
"The response was my SatNav said this way.
NYFRS also took to Twitter urging people to avoid fast flowing water, especially in the current weather conditions.
The service said: "Crews from Ripon have rescued two male occupants and a dog from a Transit van that drove into a fast flowing river when crossing a ford.
"Please avoid fast flowing water with current weather conditions as they are."
Crews from Ripon, Harrogate, Richmond and Knaresborough attended.
The Transit van was recovered using the vehicle mounted winch and level 2 water rescue equipment.