In the other two ties, there is an all-Spanish tie featuring Villareal taking on Valencia, while three-time runners-up Benfica will take on Eintracht Frankfurt.
The first legs of the ties will take place on April 11, with the return legs seven days later on April 18.
As Arsenal and Chelsea were both drawn to play at home in their second legs, UEFA regulations mean Arsenal's tie with Napoli will now be reversed, with the Gunners hosting the Italian side in the first leg instead.
Napoli, who are chasing their first European title since Diego Maradona's team won the old UEFA Cup in 1989, are currently second in Serie A, 18 points adrift of leaders Juventus.
They dropped into the Europa League after failing to qualify from a Champions League group containing Paris Saint-Germain and Liverpool. They finished on the same points total as Jurgen Klopp's side but finished third in the group by virtue of goals scored.
Chelsea boss Maurizio Sarri had stated he wanted to avoid his former club Napoli and he got his wish by drawing Slavia Prague, which shocked five-time champions Sevilla with a comeback late in extra time in the round of 16 on Thursday.
The Blues cruised into the last eight with an 8-0 aggregate win over Dynamo Kiev.
Arsenal will face Villarreal or Valencia in the semi-finals if they beat Napoli. Chelsea's semi-final opponents will be Eintracht Frankfurt or Benfica should they get past Slavia Prague.
Napoli v Arsenal
Villareal v Valencia
Benfica v Eintracht Frankfurt
Slavia Prague v Chelsea
Europa League semi-final draw
Winners of Napoli v Arsenal will play winners of Villareal v Valencia
Winners of Benfica v Eintracht Frankfurt will play winners of Slavia Prague v Chelsea