The paper, launched in September 1937, currently prints six-days-a-week. Coverage of Scunthorpe United dominates its sports coverage.
Its owners, Northcliffe Media, said on Friday that from August 18 it would only print on Thursdays.
The newspaper has sponsored the family stand at Glanford Park since its opening in 1988.
The decision comes against a backdrop of local newspapers combining resources, with many titles being produced from one production hub to reduce costs.
The Grimsby Telegraph, Hull Daily Mail, Scunthorpe Telegraph and Lincolnshire Echo are all partly designed and sub-edited by production staff in Hull.
There is speculation other papers in the group may also go weekly. The Lincolnshire Echo editor Job Grubb - a former editor of the Scunthorpe title - resigned this week in a move that Hold The Front Page suggested was linked to moves to make the paper a weekly.
Advertising revenue has been on a downward spiral in the sector, with declining circulations widespread.
Chris Sumpter, the paper's deputy sports editor, said via Twitter on Friday that no decision had been made on how its coverage of Scunthorpe United would be affected.
The paper has a larger pool of journalists covering the Iron than any other media organisation.
The Telegraph runs a specialist sport website separately from its news offering, this includes live text commentary of Iron matches but otherwise mostly runs the same content that has been published in the paper.
One possibility is that it will increase its online presence, running more breaking news on the website during the week.
Mark Price, managing director of the Grimsby Scunthorpe Media Group, hinted at likely redundancies.
"The decision has been announced to staff. A number of jobs are likely to be affected as a result of the move, but the Scunthorpe Telegraph management team has pledged to do everything it can to limit the number of compulsory redundancies," he said.