"to pretend illness to escape duty," 1820, from French malingrer "to suffer," a slang word that probably also at one time meant "pretend to be ill," from malingre "ailing, sickly" (13c.), which is of uncertain origin, possibly a blend of mingre "sickly, miserable" and malade "ill." Mingre is itself a blend of maigre "meager" (see meager) + haingre "sick, haggard," which is possibly from Germanic (compare Middle High German hager "thin").
The sense evolution in French would be through the notion of beggars who feigned to be sick or exhibited sham sores to excite compassion. Malingerer is attested from 1761, in a translation of de Saxe; malingering as a verbal noun is attested from 1778. Related: Malingered.