Etymologically, the OED says that we're not sure where the word came from exactly, except it ends in the normal English -ly adverb ending. It lists some theories:
It has been suggested that the first element is < Anglo-Norman gençur and Old French gençor , gentior , etc. (12th cent.), comparative and superlative of gent in the senses 'beautiful, pretty, pleasant', also used as a positive (13th cent.). This is formally and semantically possible, but the French forms are not attested after the end of the 13th cent., so this interpretation would assume several centuries of unrecorded survival in either French or English (perhaps as a technical term in dancing).
The earliest definition listed in the OED is this now-obsolete sense:
Chiefly with reference to walking or dancing: with small elegant steps; elegantly, daintily. Also in later use: mincingly, effeminately.
The earliest quote is:
And I can daunce it gyngerly.
A new iuterlude and a mery of the nature of the .iiii. element , ?1520
Another early quote:
With, Gingirly, go gingerly! her tayle was made of hay; Go she neuer so gingirly, her honesty is gone away.
Goodly Garlande of Laurell, 1523