The Toffees will face a trip to north London in the next round, while Manchester City's quadruple hunt sees the club drawn against holder Wigan.Roberto Martinez will need to handle a trip to Arsenal in the FA Cup quarterfinals if he is to win the competition for a second consecutive season.
Everton, which beat Swansea City 3-1 at Goodison Park on Sunday to book its place in the sixth round, claimed a 1-1 draw at the Emirates Stadium earlier this season.
Elsewhere, Gus Poyet could be set for a quick return to the Amex Stadium and former employer Brighton, with Sunderland drawn against the Seagulls or Steve Bruce's Hull City.
Quadruple-chasing Manchester City, meanwhile, will face reigning FA Cup holder Wigan Athletic at the Etihad Stadium, with Manuel Pellegrini's men having defeated Chelsea 2-0 en route to the quarters.
The draw in full:
Arsenal vs. Everton
Brighton or Hull City vs. Sunderland
Sheffield United vs. Sheffield Wednesday or Charlton
Manchester City vs. Wigan Athletic