I don’t know if this is still an issue, but since version 0.22 it seems you need to use capture groups to pass values to the rewrite-target value
From the nginx example available here
Starting in Version 0.22.0, ingress definitions using the annotation nginx.ingress.kubernetes.io/rewrite-target are not backwards compatible with previous versions. In Version 0.22.0 and beyond, any substrings within the request URI that need to be passed to the rewritten path must explicitly be defined in a capture group.
For your specific needs, something like this should do the trick
apiVersion: extensions/v1beta1
kind: Ingress
metadata:
name: myapi-ing
annotations:
ingress.kubernetes.io/rewrite-target: /api/$2
kubernetes.io/ingress.class: "nginx"
spec:
rules:
- host: api.myapp.com
http:
paths:
- path: /auth/api(/|$)(.*)
backend:
serviceName: myapi
servicePort: myapi-port