MySQL 8.0

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CREATE TABLE A (id int , json_field JSON)
INSERT INTO A VALUES(1,NULL), (2,NULL)

Records: 2  Duplicates: 0  Warnings: 0


CREATE TABLE B
    (`a_id` int, `value` int)
;
    
INSERT INTO B
    (`a_id`, `value`)
VALUES
    (1, 100),
    (1, 101),
    (2, 200),
    (2, 201)
;

Records: 4  Duplicates: 0  Warnings: 0


UPDATE A
  INNER JOIN  (
SELECT 
  a_id,
CONCAT('[',GROUP_CONCAT(`value` ),']') val
FROM B
GROUP BY a_id) t2 ON A.id = t2.a_id
SET json_field = t2.val

Rows matched: 2  Changed: 2  Warnings: 0


SELECT id,JSON_PRETTY(json_field) FROM A


id
JSON_PRETTY(json_field)


1
[
  100,
  101
]

2
[
  200,
  201
]