The store at 229-249 Buchanan Street will shut on Saturday.
Stock was being sold at heavily discounted prices with a sign on the window directing customers to the St Enoch store.
Two members of staff will lose their jobs with the majority redeployed to other stores including The Forge.
Owner Arcadia said Dorothy Perkins would be replaced by another brand, Topman, which has another store just yards away.
The company, which also owns Topshop, Burton and Miss Selfridge, said it was "constantly reviewing" its store portfolio.
Two years ago the firm agreed to close a number of stores nationwide as it battled tough conditions on the high street.
However, last year a 22% rise in internet sales and continued growth in overseas sales saw pre-tax profits rise from £133m the previous year to £167m.
A spokeswoman for Arcadia said: "Dorothy Perkins is moving out as we trade in St Enoch Centre, and Topman is moving in."