1680s, "to shake to and fro" (especially of money in a cap, as part of a game called hustle-cap), metathesized from Dutch hutselen, husseln "to shake, to toss," frequentative of hutsen, variant of hotsen "to shake." "The stems hot-, hut- appear in a number of formations in both High and Low German dialects, all implying a shaking movement" [OED]. Related: Hustled; hustling. Meaning "push roughly, shove" first recorded 1751. That of "hurry, move quickly" is from 1812.
Sense of "to get in a quick, illegal manner" is 1840 in American English; that of "to sell goods aggressively" is 1887.