Logs4j CVE-2021-44228 Vulnerability

Prometheus itself is written in Go rather than Java, so has no issue. However there are various bits of the echosystem (e.g. third party exporters) that might be using Java and therefore could have issues. So it really depends on what you are using. I’d suggest taking stock of what is being used, and then for all the pieces that are written in Java check for updated versions (if needed) from their creators.