The game was already over as a contest by the 23rd minute after Chukwueze's brace along with goals from Tijjani Reijnders and Rafael Leao handed Milan a 4-0 lead.
The intensity dropped following the interval but Milan added a fifth through Davide Calabria 11 minutes after the interval. Sassuolo did find a consolation goal with Samuele Mulattieri scoring three minutes later before Tammy Abraham rounded off the win in the 61st minute.
Chukwueze opened the scoring in the 12th minute when a Reijnders ball over the top put him through one-on-one with the keeper and after his first effort hit the upright he tapped in the rebound.
Reijnders drilled a shot home from outside the area five minutes later and Chukwueze netted his second in the 21st minute, curling a shot beyond the reach of the keeper after a Tammy Abraham lay-off.
Two minutes later, a no-look pass from Ruben Loftus-Cheek found Leao in the area and he struck a powerful shot low into the far corner.
Milan manager Paulo Fonseca's starting side had eight changes from the team which beat Empoli 3-0 at the weekend, and at the start of the second half he sent on four substitutes.
One of those replacements, Christian Pulisic, sent a lofted cross into the box which came off the post and Calabria reacted quickest to convert when the ball came back out.
Mulattieri's shot squirmed under Milan keeper Lorenzo Torriani, another half-time substitute, to finally give Sassuolo something to cheer about, but Abraham finished off the rout, tucking his finish past Sassuolo keeper Giacomo Satalino.
Meanwhile, in the other tie of the night, Bologna hammered Monza 4-0 to progress - Santiago Castro impressed with a goal and three assists.
Milan will face the winner of the last 16 tie between AS Roma and Sampdoria.