Customers and staff have been evacuated from the building, and the store is closed until further notice. A structural engineer has been called to assess the depth of the sinkhole, which has appeared in a rear alleyway.
Police have cordoned off sections of the area, and North Yorkshire Fire and Rescue are on the scene.
Harrogate Borough Council's emergency planning team have arrived.
A council spokesperson said: "I think the sinkhole is fairly sizeable for it to cause sufficient concern to call out a structural engineer."
Eyewitnesses say the sinkhole is blocking a fire escape.
A resident who lives nearby, said: "It's really scary considering how many sinkholes have happened over the last few years - Magdalens, the leisure centre, and now this. And they've all been pretty close to where I live.
"I'm in rented accommodation, so thankfully we don't have to think about the financial side of it, but it's still worrying obviously. We've noticed more cracks pop up in our walls over the seven years we've been in the house.