Here are two ways to do it, testing on MySQL 5.7.24:
mysql 5.7.24> select config from mytable
where json_contains(config, cast('[]' as json), '$.tier');
+--------------+
| config |
+--------------+
| {"tier": []} |
+--------------+
mysql 5.7.24> select config from mytable
where json_contains_path(config, 'one', '$.tier');
+--------------+
| config |
+--------------+
| {"tier": []} |
+--------------+
I found another solution, which helps to check strictly for an empty array:
First, see that I have two rows, and one has a non-empty array:
mysql 5.7.24> select config from mytable
where json_contains(config, json_array(), '$.tier');
+----------------------------------------+
| config |
+----------------------------------------+
| {"tier": []} |
| {"tier": [{"name": "BK", "value": 8}]} |
+----------------------------------------+
2 rows in set (0.00 sec)
Now I make sure that the length of the array is 0 as a way of confirming that it is empty:
mysql 5.7.24> select config from mytable
where json_contains(config, json_array(), '$.tier')
and json_length(config, '$.tier') = 0;
+--------------+
| config |
+--------------+
| {"tier": []} |
+--------------+
1 row in set (0.00 sec)