A plea was made by councillors on Sunday for people to receive Pfizer vaccines at Woodcross Health Centre in Wolverhampton without an appointment.
There were 560 vaccines available.
However, all the vaccines have now been used up and people have been asked not to turn up at the centre.
Currently only people deemed vulnerable to coronavirus or who are aged 38 or over are being offered vaccinations.
Younger people have only been able to get vaccinated when centres have supplies that need using before their expiry date and not enough eligible people to use them.
Anyone not yet eligible is being urged to wait to be contacted by the NHS before attempting to book a vaccine.
Since the vaccine programme begin in December, the NHS has gradually rolled out first vaccinations to younger groups while offering second jabs to older and vulnerable people. Some people are now being offered second doses earlier than had been planned due to concerns over the Indian variant.
Jabs are being offered via GP surgeries and at designated vaccination centres at sites like the Black Country Living Museum.
For more information, visit the NHS website.