Yes, there is a vaccine: MVA-BN vaccine
Vaccines to protect against an Mpox infection do exist, but currently no available vaccines specifically target the monkeypox virus. How is this possible?
The monkeypox virus belongs to a genus of viruses called Orthopoxvirus, which are all complex DNA viruses.
Among others, viruses in this genus include the variola virus, which causes smallpox, the cowpox virus, and the vaccinia virus.
Viruses from this genus have a great share of genetic similarity, which makes it possible for vaccines developed against other viruses to also be used to protect from Mpox infection.