Use static function as operations with batch API
The function that Drupal uses to process the batch operation is _batch_process(), which uses the following code to call the operation callback.

  // Build the 'context' array and execute the function call.
  $batch_context = array(
    'sandbox'  =&gt; &amp;$current_set['sandbox'],
    'results'  =&gt; &amp;$current_set['results'],
    'finished' =&gt; &amp;$finished,
    'message'  =&gt; &amp;$task_message,
  );
  call_user_func_array($callback, array_merge($args, array(&amp;$batch_context)));


Since call_user_func_array() allows to use a string like MyClass::myMethod as callback, the code you wrote should work, if the Drupal autoloading system is able to find the file containing the class definition, which means:


You need to respect the file structure as per the PSR4 structure expected by Drupal
You need to fully qualify the class name by adding its namespace


In the case the file containing the class it is not in the directory where Drupal looks for class files, such as in the case the class is contained in a my_operation_callbacks.inc put in the same directory containing the module file, then you need to use code similar to the example code shown in Batch operations.

$batch = array(
  'title' =&gt; t('Exporting'),
  'operations' =&gt; array(
    array('my_function_1', array($account-&gt;id(), 'story')),
    array('my_function_2', array()),
  ),
  'finished' =&gt; 'my_finished_callback',
  'file' =&gt; 'path_to_file_containing_myfunctions',
);


$batch['file'] in that code tells Drupal which file it needs to load before executing the operation callbacks.
Even in this case, the class must be referenced using its namespace, which could simply be \ in the case the class is put in the global namespace.