From Greek morphḗ, "form, shape" + -ology, via French and German. (Oxford English Dictionary)
In the sense in which this term is used in Linguistics — for the study of word forms or word structure — morphology was borrowed into English from German Morphologie, which was introduced in Schleicher (1859). Here is the opening sentence of Schleicher's article, with my translation:
Den gegenständ der morphologie der spräche bildet die lautliche form des wortes, seine äußere gestalt, d. h. das vorhandensein oder felen seiner teile und die stellung, welche dise teile ein nemen; unberüksichtigt laßen wir das material, auß dem das wort gebildet ist, den klang der zum aufbau desselben verwanten lautelemente.
(The object of the morphology of language is composed of the phonetic form of the word, its outward shape, i.e. the presence or absence of its parts and the position which these parts occupy; regardless, we leave off the material from which the word is formed, the sound of the phonetic elements related to the construction of the same.)
Note: Schleicher employs some non-standard capitalization and spelling conventions here.
Schleicher's formulation is not as clear as one would hope for; it strikes me, at least, as somewhat odd to define morphology in terms of "phonetic form" but then to set aside "the sound of phonetic elements."
Undoubtedly, Schleicher was building on the already-established use of Morphologie in biology, for the study of the forms of organisms. This use of the term appears to be due to Goethe, and dates to the 1790s.
The earliest use in English of morphology in the linguistic sense appears to be in Farrar (1870).
- Farrar, Frederic William (1870) Families of Speech: Four Lectures Delivered Before the Royal Institution of Great Britain in March, 1869. London: Longmans.
- Schleicher, August (1859) Zur Morphologie der Sprache. Mémoires de l'Académie impériale des sciences de St.-Pétersbourg 1.7.1–38.