Paul Scherer, aged 57, from Seacroft, was last seen yesterday at about 9.15am when he drove off after stopping on the M1 towards Wetherby.
He was driving a black Peugeot 407 saloon, registration CK08WVE.
Mr Schere is described as white, 5ft 7ins to 5ft 8ins tall, and of slim build. He was wearing a navy Leeds United coat, jeans and blue trainers.
He has links to the Filey area of North Yorkshire.
Detective Inspector James Entwistle, of Leeds District CID, said: “We are concerned for Paul’s welfare given the circumstances in which he has gone missing and we urgently need to find him so that we can check he is okay.
“We are carrying out extensive enquiries to trace him and we would like to hear from anyone who has seen him or his car at any point since yesterday morning.”
Anyone with information is asked to contact officers via 101 quoting log number 1079 of December 26.