"Humpty-Dumpty" was considered to be a riddle in Halliwell, "The Nursery Rhymes of England," 1846 (on line).

7th Class, Riddles
CXXXV
(An Egg)
Humpty Dumpty sate on a wall,
Humpty Dumpty had a great fall;
Three score men and three score more
Cannot place Humpty Dumpty as he was before.
(this is from 1810)

He appears in Europe as Humpelkin-Pumpelkin (Germany), and other names.

Humpelkin-Pumpelkin sat up de Bank,
Humpelkin-Pumpelkin fel von de Bank;
Do is ken Doktor in Engelland
De Humpelkin-Pumpelkin kurere kann.
(Saxony)
Bank = bench; there is no doctor in Engelland who can restore H-P. Engelland = 'angel land.'
From Lina Eckenstein, 1906, "Comparative Studies in Nursery Rhymes." Also on line.
Eckelstein goes into the symbolism of the egg, but any relationship of these old myths to this riddle-rhyme is speculative on her part.