Notices have been attached to the chain’s branches across the country announcing: “All outlets have closed for business permanently.”
The Scarborough branch moved into the Brunswick Centre this year, from its previous home in Newborough.
It is believed it closed down on Saturday morning.
The shop was one of the Bradford-based firm's branches which chiefs announced would stay open after the firm went into administration in October 2017.
Founded in 1860, at its peak in the 1990s there were around 200 branches of the store.
Greenwoods was sold to Versatile International Trading 16 months ago in a move which was aimed at safeguarding 40 stores and 181 jobs. But notices have since been posted in windows of branches around the country announcing closure.
A sign on shop doors said: "All outlets of Versatile International Trading Ltd t/a Greenwoods Menswear have now closed for business permanently."
The sign said the company had voluntarily gone into liquidation.