A problem with the system meant that people were able to book appointments over the weekend despite clinics being closed.
Work is taking place to resolve this issue.
Any adult with a rescheduled appointment for a date any day this week is being asked not to attend.
This will be an appointment they have been able to reschedule through the national appointing system.
The only clinics running between Monday 4 April up to Sunday 10 April are first dose vaccination clinics for young people aged five to 11.
Dr Nigel Calvert, Vaccination Co-ordinator for NHS Dumfries and Galloway said: "Very sincere apologies are extended to everyone impacted by the issues experienced with rescheduled appointments.
"No clinics for rescheduled adult appointments are running in the region this week, and we’re continuing to work with the national appointing team in order to resolve this issue around incorrect appointments and ensure that the situation is not repeated.
"Everyone who has been provided a rescheduled appointment for this week should now be being contacted directly in order to see this addressed – and being provided with the next available correct slot."
He explained that they are looking into how appointments were able to be made that were not available to ensure it doesn't happen again.
He added: "People have been hugely receptive to the Covid vaccination programme in Dumfries and Galloway, and the uptake has undoubtedly played a massive role in helping to prevent the worst possible effects of the virus among most people.
"The last thing we want to do is let anyone down, and our vaccination teams are heartfelt in this expression of apology."