Shoppers have been evacuated from Tesco on Magdalen Street.
Staff and customers were seen streaming out of the Express store at around 9.50am.
Pictures from the scene show customers milling around the entrance, seemingly unable to enter the shop.
A customer told us shoppers were asked to leave the store after the fire alarm sounded.
She said: "The alarm went off and no one really knew whether to leave or not. But staff quickly ushered us out.
"There was no panic - some people were actually a bit annoyed."
She said around 50 people were now waiting outside St Mary Magdalen's Church which she assumed was a fire assembly point.
Tesco and Oxfordshire Fire and Rescue Service have been approached for comment.
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