The fire service said the van was stranded on the A281 at Henfield in floodwater from the River Arun, which has burst its banks.
A technical rescue unit, a crew from Worthing and Sussex Police were all involved in rescuing the three people.
The fire service said in a tweet: “Please do not take chances with floodwater.”
Horsham Police has also tweeted a video of a damaged car, warning people not to risk driving through floodwater.
The M23, which was closed for several hours, has now reopened but the A29 is closed at Pulborough due to the flooding.