The Health Service Executive said all available appointments for the monkeypox vaccine were full.
It comes after 11 designated vaccination centers opened across the country today.
The HSE said demand for the vaccine was high and more appointments would be available early next month.
Last week the HSE said it intends to complete monkeypox vaccinations for high-priority groups by the end of the year.
The HSE estimates that between 6,000 and 13,000 people would benefit from a primary prevention vaccine against monkeypox.
To date, more than 2,000 vials of monkeypox vaccine have been purchased.
In August, the European Medicines Agency also said the vaccine could be delivered intradermally, meaning vials of the vaccine can go further and deliver more doses.
According to the EMA, one vial can provide five doses. In practice, the committee was informed that vaccine administrators typically receive four doses per vial.
Two doses of the monkeypox vaccine are given at least 28 days apart.
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