Tottenham, who beat fierce local foes Arsenal 2-0 at the Emirates Stadium to reach the semis, have also played London clubs Watford and West Ham in this year's competition.
"A very difficult draw, another London derby," Tottenham manager Mauricio Pochettino told Sky Sports.
"We shall see, Chelsea are a great team but we are excited. To be in the semi-final is fantastic for us."
Chelsea booked their spot in the last four with a 1-0 win over Bournemouth thanks to Eden Hazard's deflected winner.
Burton reached the semi-finals for the first time in their history after Nigel Clough's side beat Middlesbrough 1-0 on Tuesday.
They face the daunting prospect of trying to stop Premier League champions Manchester City, who beat Leicester City on penalties to reach the last four.
The two-legged ties will be played in the weeks of Jan. 7 and Jan. 21.
(Reporting by Toby Davis,; Editing by Ed Osmond)
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