Huddersfield town centre's My Local store is set to close.
And about 20 staff at the convenience store in King Street face redundancy after the business was put into administration.
Ninety of the chain’s 125 stores, including the King Street store, face closure with the loss of more than 1,000 jobs.
Another 32 outlets will continue to trade and have potential buyers while two stores have already been sold.
Joanne McGuinness, national officer for shopworkers’ union Usdaw, said: “My Local staff are deeply disappointed by the news that the company has gone into administration.
“We continue to talk with the company about the future of the remaining stores as we seek to see them successfully transferred to new owners.
“We are also in conversation with Morrisons who have offered to re-employ any former staff who have lost their jobs as a result of My Local store closures.
“In the meantime, we continue to provide our members with the support, advice and representation they need.”
Morrisons sold 140 M Local shops for £25m last September to retail entrepreneur Mike Greene, who rebranded them My Local.
Morrisons opened the King Street store in March 2014.
Mark Orton, partner at KPMG and joint administrator at My Local, said: “Since taking over the business in October last year, management have faced tough trading conditions and despite their best efforts to improve performance, My Local was ultimately unable to return to viability.
“Having explored a number of other options, the directors were unable to find a way forward and took the difficult decision to place the company into administration.”