There's been reports that some women aren't attending appointments to not overburden the NHS.
Oxford University Hospital says its maternity service is still open 24/7 for births, urgent care, and clinical advice.
High risk antenatal clinics in the Horton and John Radcliffe Hospital and the ultrasound departments are running too.
The Trust, which runs four hospitals in Oxford, has made changes to its service because of the coronavirus which includes carrying out some appointment by telephone or video.
Catherine Greenwood, Consultant Obstetrician and Clinical Director for Maternity at the Trust said: "It is really important that women [sic] stay in contact with their maternity team and attend their scheduled appointments.
Miss Greenwood added: "As we can all understand, many people have anxieties around their health during this very unusual time – especially pregnant women.
"Some women may feel afraid to leave their homes to attend appointments or to come to hospital as they have concerns around getting COVID-19. Similarly, we have heard reports of some women not attending appointments.
"We will use the appropriate measures to keep you safe from infection every time we see you. In addition, wherever we can we will do these appointments remotely. We’re here for you, day or night, if you have concerns about your health or your unborn baby’s wellbeing.
"If any women are worried about not attending their appointments because they’re self-isolating, please rest assured that we will offer new appointments for when it ends. If you have an urgent problem, you can speak to a midwife or doctor day or night at our Maternity Assessment Unit."