The ballot follows an announcement from the publisher that it intends to make 18 editorial redundancies across its South Yorkshire titles.
Staff were informed last week of plans to close the office of the Goole Courier and scrap the editor's role at both the Courier and South Yorkshire Times, leaving a single editor based at the Selby Times' office to manage all three titles.
The NUJ chapel cited a number of reasons for the no-confidence vote, including "serious on-going strategic mismanagement of the business" and "disgraceful mismanagement at divisional and local level".
NUJ northern and midlands organiser Chris Morley said: "Management's proposals show how flimsy are the Johnston Press claims to believe in local journalism to serve the communities where its newspapers circulate.
"The company has chosen to attack the editorial department of one of the best performing titles for circulation in its stable. The South Yorkshire Times has fought hard for its reputation as a campaigning newspaper that digs out stories people want to read but this seems to cut no ice with the corporate bean counters.
"Our members are in no mood to accept these wholesale cuts which merely undermine the jobs that remain for the future. It is a disastrous blend of hopelessness and defeatism and shows that Johnston Press has no idea or strategy to grow the business or defend its staff and customers with a positive strategy."
The company was unavailable for comment this morning, but managing director John Bills said last week said that despite a planned reduction of 18 jobs there eight equivalent roles vacant across Sheffield Newspapers, South Yorkshire Newspapers and Wilfred Edmunds and employees will be encouraged to apply for the vacancies.
Bills said: "Prior to any implementation, management will consult extensively on an individual and collective basis.
"In the event these plans go ahead, the company will endeavour to minimise the impact through re-deployment to alternative positions across Johnston Press and voluntary redundancy."
Johnston Press is now in a 30-day consultation with affected staff over the proposed cuts.