Hastings Borough Council said it was told there was a technical issue with the ambulance, meaning the clinic had to be delayed.
The Sussex Health and Care Partnership, who are running walk-in clinics across Sussex, hope to return to the former Debenhams store, in Robertson Street, on Thursday (July 29).
The clinic will run from 11.30am until 3pm on Thursday.
There will also be another walk-in clinic outside Tesco Extra, in Church Wood Drive, St Leonards between 3.30pm and 6.30pm on Thursday.
Then on Friday (July 30), the team will be back at Debenhams between 11.30am and 6.30pm. They will also be there between 11.30am and 6.30pm on Saturday (July 31).
For all four walk-in clinics, all adults have been invited to attend. You are eligible if you are receiving your first jab or your second jab, as long as there have been eight weeks since your first jab. The clinics will all be offering the Pfizer vaccine.