You can use MongoDB_DataObject wrapper to perform such query like below:
$model = new MongoDB_DataObject('orders');
$model->whereAdd('MONTH(created) = 4 AND YEAR(created) = 2016');
$model->find();
while ($model->fetch()) {
var_dump($model);
}
OR, similarly, using direct query string:
$model = new MongoDB_DataObject();
$model->query('SELECT * FROM orders WHERE MONTH(created) = 4 AND YEAR(created) = 2016');
while ($model->fetch()) {
var_dump($model);
}