Prometheus itself can read a properly-shaped JSON file with file_sd_config:

- job: foo
  file_sd_configs:
  - files:
    - /opt/monitoring/example.json

The format of the JSON file should be like this:

[
  { "targets": [ "<host>", ... ], 
    "labels": { "<labelname>": "<labelvalue>", ... }
  }, 
  ... 
]

If you need to generate the file, you can modify container startup command so that it will create the file prior starting Prometheus:

containers:
- name: prometheus
  image: prom/prometheus
  command: ["/bin/sh", "-c"]
  args: 
  - echo '[{"targets":["example.com"],"labels":{"foo": "bar"}}]' > /tmp/filesd.json && prometheus --arg1 --arg2

Alternatively, if you need to repeat the command to generate the file, consider using cron (you have to add it to the image and start as a service before Prometheus).

At last, you can make a simple app that will expose the same JSON over HTTP and run the app alongside Prometheus (in the same pod). In such case you will need http_sd_config.