Both clubs knocked out lower-league opposition on Wednesday to set up a two-legged meeting in the last four, with the matches set to be played in January 2020.
Rashford starred in a comfortable 3-0 victory over Colchester United at Old Trafford, extending his fine run of form by scoring his 14th club goal of the season.
The England striker was also on target when United recorded a shock 2-1 win against Premier League champions City at the Etihad Stadium earlier this month.
Rashford has a strong record in the derby having also hit the winner in the fixture during his breakthrough campaign at United.
The 22-year-old is looking forward to the next chapter of one of football's historic rivalries.
"Made to work for it but job done tonight getting into semis," Rashford wrote on Twitter after United's defeat of Colchester midweek.
"Bang up for another derby too. Best games to play. Best games to win."
United's last EFL Cup title was in the 2016-17 season when they beat Southampton in the final.
City has won the tournament in three of the past four years, including each of the past two seasons.