From Middle Low German schüchter, whence also Dutch schuchter. Cognate with scheu. The final -n is an original case ending, which was sometimes added to the stem in Low German (compare German albern).
The words scheu and schüchtern both translate into English as “shy”. Although they are sometimes synonyms in German as well, there is generally a subtle distinction: scheu means “avoiding contact with others”, whereas schüchtern means “feeling uncomfortable or awkward in contact with others”. (Hence, one's being schüchtern may but need not lead to one's becoming scheu.)