The striker took his tally for the season to 22 goals in all competitions as United seized the advantage in the first leg of the last-32 clash.
Ibrahimovic proved to be the scourge of Saint-Etienne during his trophy-laden spell at Paris Saint-Germain before moving to United last summer.
And the Swede found more joy against Christophe Galtier's side on Thursday to ensure United are favourites to reach the last 16 of the competition.
Ibrahimovic's hat-trick means he has now scored 17 goals in his last 14 games against Saint-Etienne, while he has also been involved in 17 goals (11 goals, 6 assists) in 17 appearances at Old Trafford this season.
3 - Zlatan Ibrahimovic has scored his first Manchester United hat-trick. Treble. pic.twitter.com/bA986bKv0G— OptaJoe (@OptaJoe) February 16, 2017
The hat-trick was also Ibrahimovic's first since joining Jose Mourinho's side, and the 35-year-old will now be keen to add more goals to his name before the end of the campaign.
United take on Saint-Etienne in the return leg in France on 22 February at Stade Geoffroy-Guichard.