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
  name: some-ingress
  annotations: nginx
    # Change 5m to whatever size you want 5m
    # In newer versions of nginx-ingress, you'll need this instead 5m