There's a proxy-body-size option that can be configured via an annotation on ingress objects. This option maps to client_max_body_size in the nginx configuration.
edit: There is now an actual client-max-body-size annotation.
---
apiVersion: extensions/v1beta1
kind: Ingress
metadata:
name: some-ingress
annotations:
kubernetes.io/ingress.class: nginx
# Change 5m to whatever size you want
nginx.ingress.kubernetes.io/proxy-body-size: 5m
# In newer versions of nginx-ingress, you'll need this instead
nginx.org/client-max-body-size: 5m
spec:
...