1530s, "put together hastily," probably from Middle English shovelen "to move with dragging feet," itself probably a frequentative form of shoven (see shove (v.) and compare scuffle). Or perhaps from Low German schuffeln "to walk clumsily, deal dishonestly."
In reference to playing cards in a pack, "change the relative position of so that they may fall to players in an irregular and unknown order," it is recorded by 1560s, frequently figurative. The meaning "move the feet along the floor without lifting them" is from 1570s.
The meaning "push along gradually, shove little by little" is from 1560s. The meaning "move from one place to another" is from 1690s. The sense of "do a shuffle dance" is by 1818 (Scott, in reference to a dancing bear). Related: Shuffled; shuffling. To shuffle off "get rid of, dispose of" is from Shakespeare (1601).