Drupal - How to restrict a module to a specific core version?

Using core only supports the major version, but you can add a dependency on the system.module with a specific version.

dependencies:
 - system (>=8.3)

Due to a bug in version parsing, you can only do this with the minor version. You can't specify a patch release like 8.3.1.

You can check in hook_requirements like so:

function mymodule_requirements($phase) {
  // code
  $version = \Drupal::VERSION;
  // code that checks version info here

  return $requirements;
}

If $version is not what you're expecting, throw a REQUIREMENT_ERROR. In fact, there is sort of an example on the docs page.

function mymodule_requirements($phase) {
  $requirements = [];

  // code
  $version = explode('.', \Drupal::VERSION);
  // code that checks version info here

  if ($version[0] == 8 && $version[1] < 3) {
    $requirements['mymodule'] = [
      'title' => t('My Module'),
      'description' => t('This module requires Drupal 8.3.0 or higher before it can be installed.'),
      'severity' => REQUIREMENT_ERROR
    ];
  }

  return $requirements;
}