The latest figures for the city show a doubling of cases to a rate of 43.9 per 100,000 people.
Oxford is currently on amber alert, but is edging closer to red alert level according to the County Council.
The Covid-19 cases are across all parts of the city, mostly among 18 to 24-year-olds and cases per 100,000 are now at their highest level in Oxford since May.
Meanwhile cases for Oxfordshire as a whole are currently yellow with cases 18.1 per 100,000.
Ansaf Azhar, Oxfordshire County Council’s Director for Public Health, said: “We have seen a considerable increase in cases in Oxford.
“While this mirrors what is happening nationally, we must remember that cases in Oxford have doubled over the past week and the situation can deteriorate further very quickly. If we don’t all take this very seriously, we risk seeing tough local restrictions imposed that none of us want.
"We have recently seen many other parts of the country go into lockdown. This is something we all want to avoid. But if cases continue to rise at the rate they have been doing, then we may have no choice."
“My plea is a simple one – keep your distance, wash your hands, wear a mask, and ensure you are adhering to the rule of six.
“It’s up to all of us to bring the virus under control. The latest figures are a stark warning that we must act now. We need to slow the rate before it’s too late.”
Last week it was revealed that 30 new coronavirus cases had been confirmed at Oxford Brookes University, in the space of just one week.
#COVID19 cases in Oxford have doubled in the last week. #stopthespread:— Lord Mayor of Oxford (@OxfordLordMayor) September 30, 2020
1. Keep your distance
2. Stick to the rule of 6
3. Wash hands regularly with soap & water
4. Wear a face covering
5. Symptoms? Self-isolate & get tested
6. Download NHS COVID-19 apphttps://t.co/l4ut8Ynxjx