I'm trying to exec into haproxy-ingress pod created from this image, with this command:
kubectl -n kube-system exec -it haproxy-ingress-4122301161-bcd94 /bin/bash
Then I get this message
rpc error: code = 13 desc = invalid header field value "oci runtime error: exec failed: container_linux.go:247: starting container process caused \"exec: \\"/bin/bash\\": stat /bin/bash: no such file or directory\"\n"
Is there a way to exec into a container that is created using an image that does not have bash pre-installed?
Yes, it's not that uncommon for container not to have bash available. Often you will find that when bash is not there, /bin/sh still is, as is the case for the image you mention. Thus using kubectl -n kube-system exec -it haproxy-ingress-4122301161-bcd94 /bin/sh should suffice.
That aside, please mind for sake of clarity, you do not SSH into container, you execute a process within it.