I had to run this for a column introduced in the later stages of a product, on 10+ tables. So wrote this quick untidy script to generate the alter command for all 'relevant' tables.
SET @NeighboringColumn = '<YOUR COLUMN SHOULD COME AFTER THIS COLUMN>';
SELECT CONCAT("ALTER TABLE `",t.TABLE_NAME,"` CHANGE COLUMN `",COLUMN_NAME,"`
`",COLUMN_NAME,"` ", c.DATA_TYPE, CASE WHEN c.CHARACTER_MAXIMUM_LENGTH IS NOT
NULL THEN CONCAT("(", c.CHARACTER_MAXIMUM_LENGTH, ")") ELSE "" END ," AFTER
`",@NeighboringColumn,"`;")
FROM information_schema.COLUMNS c, information_schema.TABLES t
WHERE c.TABLE_SCHEMA = '<YOUR SCHEMA NAME>'
AND c.COLUMN_NAME = '<COLUMN TO MOVE>'
AND c.TABLE_SCHEMA = t.TABLE_SCHEMA
AND c.TABLE_NAME = t.TABLE_NAME
AND t.TABLE_TYPE = 'BASE TABLE'
AND @NeighboringColumn IN (SELECT COLUMN_NAME
FROM information_schema.COLUMNS c2
WHERE c2.TABLE_NAME = t.TABLE_NAME);