EntityFieldQuery class doesn't have any method for that and I tried to use hook_query_alter but no luck there too.
This is currently not possible (Drupal 7.43). EntityFieldQuery doesn't have any options for using a slave/replica database, nor does the module that actually executes the query, which is field_sql_storage.module in field_sql_storage_field_storage_query().
Ultimately that function calls db_select():
$select_query = db_select($tablename, $table_alias);
But it doesn't pass the 3rd parameter which is where the slave database would be targeted, so it will always use the master. It's also not possible to alter the query to add new options, as the
Query->queryOptions property is protected.
I filed an issue against Drupal core, if it gets fixed the solution will be posted there: https://www.drupal.org/node/2714021