MySQL 8.0

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CREATE TABLE test (
  id INT,
  col_json JSON
);
INSERT INTO test VALUES 
  (1, '["2016-04-21", "2016-04-22"]'),
  (2, '["2016-04-21", "2016-04-26"]'),
  (3, '["2016-04-22", "2016-04-26"]'),
  (4, '["2016-04-26"]');

Records: 4  Duplicates: 0  Warnings: 0


SELECT * 
FROM test 
WHERE NOT JSON_SEARCH(col_json, 'all', '2016-04-22') IS NULL;


id
col_json


1
5b22323031362d30342d3231222c2022323031362d30342d3232225d

3
5b22323031362d30342d3232222c2022323031362d30342d3236225d

id	col_json
1	5b22323031362d30342d3231222c2022323031362d30342d3232225d
3	5b22323031362d30342d3232222c2022323031362d30342d3236225d