Radio Sheffield announced today that the club had refused to accept a 10 per cent reduction in fees paid for coverage rights.
The BBC asked 62 Premier League and Football League clubs for the reduction and Sheffield Wednesday was the only one not to agree to the cut.
Radio Sheffield bosses said there will be no live commentary of any Owls games.
Wednesday currently provides live commentary of home games but now plans to do the same for away games.
The club said: "Sheffield Wednesday can inform supporters that following recent discussions with the BBC, live commentary of our away fixtures will not be broadcast on Radio Sheffield during the 2018/19 season.
"The terms offered by the BBC to the club were significantly less than those within the year by year contract historically signed every summer.
"This development was unprecedented and despite our best efforts to seek a renewal only on the same terms, agreement could not be reached."
The club added: "The club has been told by the BBC of our extremely healthy audience figures and when aligned with our media profile that has grown hugely in recent years, we do not believe a reduction in terms is appropriate.
"This, combined with regular subscriber feedback, has now afforded the Owls the opportunity to launch a brand new strand of our iFollow service for the club’s away games and match those at Hillsborough.
"Sheffield Wednesday are one of the most successful clubs on the EFL Digital platform, with our exposure at an all-time high and we firmly believe this development represents an exciting opportunity to take our iFollow product to the next level.
"We also believe that should our model succeed, EFL peers may seek a similar route in the future.
"Starting on Saturday at Wigan when the curtain rises on the new campaign, Wednesdayites around the world can listen to exclusive live commentary of the Latics v the Owls with a bespoke SWFC angle.
"The full game at the DW Stadium will be broadcast through iFollow Wednesday, with the whole 90 minutes live and uninterrupted.
"Our commentaries from Hillsborough with Rob O’Neill and John Pearson have long been extremely popular, leading to requests to extend the coverage away from home.
"And this season we will be doing exactly that, with the team strengthened by EFL and talkSPORT commentator Jack Woodward, who kicks off the show on Saturday alongside ex-Owls striker Pearson."
It costs Â£4.49 per month to subscribe.
Sheffield United, Rotherham, Barnsley and Doncaster matches will all continue to be covered live by BBC Radio Sheffield.
A radio station spokesman said: "We are disappointed Sheffield Wednesday hasn’t accepted the new commentary deal.
"We have a long history with the club and have enjoyed bringing fans live commentary of The Owls’ home and away fixtures.
"We’re sad we will no longer be able to provide this service.
"We want to work with the club in the future and will continue to provide the latest news about Sheffield Wednesday to our listeners.
"We will also continue to have commentaries from Sheffield United, Rotherham United, Doncaster Rovers and Barnsley."
BBC Radio Sheffield has provided live commentary on Owls games every season since 2000.
It will continue to provide score flashes from games along with pre and post-match summaries.