mySQL SELECCIONA los próximos cumpleaños

Para obtener todos los cumpleaños en los próximos 7 días, agregue la diferencia de años entre la fecha de nacimiento y hoy a la fecha de nacimiento y luego busque si cae dentro de los próximos siete días.

SELECT * 
FROM  persons 
WHERE  DATE_ADD(birthday, 
                INTERVAL YEAR(CURDATE())-YEAR(birthday)
                         + IF(DAYOFYEAR(CURDATE()) > DAYOFYEAR(birthday),1,0)
                YEAR)  
            BETWEEN CURDATE() AND DATE_ADD(CURDATE(), INTERVAL 7 DAY);

Si desea excluir los cumpleaños de hoy, simplemente cambie > a >=

SELECT * 
FROM  persons 
WHERE  DATE_ADD(birthday, 
                INTERVAL YEAR(CURDATE())-YEAR(birthday)
                         + IF(DAYOFYEAR(CURDATE()) >= DAYOFYEAR(birthday),1,0)
                YEAR)  
            BETWEEN CURDATE() AND DATE_ADD(CURDATE(), INTERVAL 7 DAY);

-- Same as above query with another way to exclude today's birthdays 
SELECT * 
FROM  persons 
WHERE  DATE_ADD(birthday, 
                INTERVAL YEAR(CURDATE())-YEAR(birthday)
                         + IF(DAYOFYEAR(CURDATE()) > DAYOFYEAR(birthday),1,0)
                YEAR) 
            BETWEEN CURDATE() AND DATE_ADD(CURDATE(), INTERVAL 7 DAY)
     AND DATE_ADD(birthday, INTERVAL YEAR(CURDATE())-YEAR(birthday) YEAR) <> CURDATE();


-- Same as above query with another way to exclude today's birthdays 
SELECT * 
FROM  persons 
WHERE  DATE_ADD(birthday, 
                INTERVAL YEAR(CURDATE())-YEAR(birthday)
                         + IF(DAYOFYEAR(CURDATE()) > DAYOFYEAR(birthday),1,0)
                YEAR) 
            BETWEEN CURDATE() AND DATE_ADD(CURDATE(), INTERVAL 7 DAY)
     AND (MONTH(birthday) <> MONTH(CURDATE()) OR DAY(birthday) <> DAY(CURDATE()));

Aquí hay una DEMO de todas las consultas