There are such references in the Upanishads as well as in the Tantras.
From the SAriraka Upanishad (one of the 108 Upanishads and it is linked with the Krishna Yajurveda):
OM. The body is a compound of prthivi (earth) and other mahabhutas
(primordial elements, as apas or water, agni or fire, vayu or air, and
akas ). (In the body), that which is hard is (of the essence of) earth
; that which is liquid is (of the essence of) water; that which is hot
is (of the essence of) fire ; that which moves about is (of the
essence of) vayu ; that which is perforated is (of the essence of)
akas . The ear and others are the jnanendriyas (organs of sense). The
ear is of the essence of akas , the skin of the essence of vayu, the
eye of the essence of fire, the tongue of the essence of water, and
the nose of the essence of earth ; sound, touch, form, taste, and
odour being respectively the objects of perception for these or gans.
These arose respectively out of the primordial elements, beginning
with earth. The mouth, the hands, the legs, the organs of excretion
and the organs of generation are the karmendriyas (or organs of
action). Their functions are re spectively talking, lifting, walking,
excretion, and enjoyment. Antahkarana (or the internal organ) is of
four kinds manas, buddhi, ahankara, and chitta. Their functions are
respectively sankalpa-vikalpa, (or will-thought and doubt),
determination, egoism, and memory. The seat of manas is the end of the
throat, that of buddhi the face, that of ahankara the heart, and that
of chitta the navel. The bone, skin, nadis, nerves, hair, and flesh
are of the essence of earth. phlegm, blood, sukla (or sperm), and
sweat are of the essence of water. Hunger, thirst, sloth, delusion,
and (desire of) copulation are of the essence of fire. Walking,
scratching, opening and closing the gross eyes, etc., are of the
essence of vayu. Desire, anger, avarice, delusion, and fear are of the
essence of akas . Sound, touch, form, taste, and odour are the
properties of earth : sound, touch, form, and taste are the properties
of water : sound, touch, and form, are the properties of fire : sound
and touch are the properties of vayu : sound alone is the property of
akas .
This is from the first chapter of the Upanishad.
The Grabha Upanishad (which is another minor Upanishad and also linked with the same Veda) also have the references:
OM. The body is composed of the five (elements) ; it exists in the
five (objects of sense, etc.); it has six supports: it is associat ed
with the six gunas ; it has seven dhatus (essential ingredients) and
three malas (impurities); it has three yonis (wombs) and is formed of
four kinds of food. Why is the body said to be composed of five ?
Because there are five elements in this body (viz.), prthivi, apas,
agni, vayu, and akas . In this body of five elements, what is the
prthivi element ? what apas ? what agni ? what vayu ? and what akas ?
Prthivi is said to be that which is hard ; apas is said to be that
which is liquid ; agni is said to be that which is hot ; vayu is that
which moves ; akas is that which is full of holes (or tubes 2). Of
these, prthivi is seen in supporting (objects), apas in cohesion,
tejas (or agni) in making forms visible, vayu in moving, akas chiefly
in avakas a (viz.j giving space). (Then what are the five objects of
sense, etc. ?) The ear exists in sound, the skin in touch, the eye in
forms, the tongue in taste, and the nose in odour. (Then) the mouth
(exists) in speech, the hand in lifting, the feet in walking, the anus
in excreting, and the genitals in enjoying. (Then) through buddhi, one
knows and determines ; through manas, he thinks and fancies ; through
chitta, he recollects ; through ahankara, he feels the idea of I .
Thus these perform their respective functions.
The Tantras also discuss this aspect.
Quoting from the ShAktAnada Taranigini's (an overview of this text can be found here) 1st chapter:
asthi charma tathA nAdi loma mAmsa tathaiva cha |
ete pancha gunAh
proktAh prithivyAncha vyAvasthitAh ||
malamutra tathA shukram
shleshmA shonitameva cha |
ete pancha gunAh proktA Apastatra
vyAvasthitAh ||
kshudhA trishnA tathA nidrA pramohah kshAntireva
cha |
ete pancha gunAh proktAstejastatra vyavasthitam ||
virodhAkshepanAkunchadhArnam tarpanam tathA |
ete pancha gunAh
proktA mArute cha vyavasthitAh ||
rAgo dveshacha mohashcha bhayam
lajjA tathaiva cha |
ete pancha gunAh proktA AkAshe cha
vyavasthitAh ||
Bones, skin, the NAdis, body hairs and flesh - These five are from the
Earth element and they are established in the Earth. The faeces,
urine, semen, phlegm and blood - These five are from the Water element
and it is established in all of those. Hunger, thirst, sleepiness,
delusion (Moha) and tiredness- These five are the properties of Fire
and it is established in all of those. Obstruction, Akshepan (unable
to translate this one, probably remorse or expansion?), Akunchan
(contraction, writhing and bending like acts), holding and contentment
- These five are the properties of the Air and they all stay in it. Anger, jealousy, delusion, fear and shame- These five are the
properties of Ether and they all stay in it.
Now, a somewhat different list is found in the Brahma GyAna Tantram which is quoted in the ShArada Tilakam. Here the mapping is like:
Bone, flesh, skin, nerve and hair.
Saliva, urine, semen, blood and marrow.
Hunger, thirst, fear, sleep, lethargy and tiredness.
Swift movement, jump, eating, contraction and expansion.
Anger, jealousy, shame, fear and delusion.
Therefore, in this way, correspondences have been established between everything that's within our body and one or the other MahAbhutas. So, that's why it's said that our body is nothing but a combination of those Pancha MahAbhutas.