Coun Gordon was elected to represent the Knottingley ward in the 2019 local elections, becoming the first Lib Dem member on Wakefield Council for eight years.
His mother, Adele Hayes, was subsequently elected to the same ward, in this year's polls.
Confirming the news on Twitter, Coun Gordon said: "I am pleased to announce that I am standing as the Liberal Democrat candidate at the Batley & Spen by-election.
"I wish Jo well, following what must have been a difficult decision to stand down."
The by-election, which was triggered by the area's former MP Tracy Brabin becoming the first elected mayor of West Yorkshire, will take place on July 1.
Other candidates confirmed to be standing include Kim Leadbeater, the sister of the late Jo Cox, for Labour.
Leeds councillor Ryan Stephenson is contesting the seat for the Conservatives, while George Galloway is also standing for his Worker's Party of Britain.
Ross Peltier for the Greens, Corey Robinson for the Yorkshire Party and independent Jayda Fransen, the former deputy leader of the far-right Britain First movement, will also be on the ballot paper, along with Paul Bickerdike from the Christian People's Alliance.
Local Democracy Reporting Service