The 58-year-old man from South Shields was arrested on suspicion of drink-driving, and has been released under investigation while police continue their inquiries.
A 76-year-old woman from Billingham died as a result of the crash, having been treated for three days at James Cook University Hospital, in Middlesbrough.
The crash took place on the northbound carriageway of the A19 near Osmotherley, in North Yorkshire, just before the A172 turn-off to Stokesley.
Police say it happened last Friday at about 7pm, with a white Citroen Dispatch van and a red Kia Rio car involved.
A statement from North Yorkshire Police added: "It is believed the collision occurred when the van crossed over from lane two to lane one as the Kia that was travelling in lane one.
"The Kia came to rest by a road-side tree.
"The passenger in the Kia, a 76-year-old woman from Billingham, died on Monday at James Cook University Hospital in Middlesbrough.
"She had to be airlifted to hospital.
"The driver of the Kia, a 40-year-old man from Stockton-on-Tees, escaped with minor injuries.
"He was also treated at the same hospital."
Police are appealing for anyone with dash-cam footage to come forward.
The force added: "The driver of the van, a 58-year-old man from South Shields, was arrested on suspicion of drink-driving.
"He has been released under investigation while police inquiries continue.
"Officers are appealing for witnesses and information to assist the investigation.
"In particular, they are urging lorry drivers and other motorists who were on A19 between the A172 Stokesley and Osmotherley turn-offs on Friday evening, to check their dash-cams in case they have any footage that could help inquiries.
"Please contact North Yorkshire Police on 101, select option 2, and ask for Hamish Halloway, or email [email protected] quoting reference number 12180111678."