Arsenal were pitted against Fenerbahce, whose presence has been overshadowed by a domestic match-fixing scandal which could still lead to the Turkish side being expelled.
Germany's Schalke 04 were paired with Metalist Kharkiv, who face a UEFA disciplinary hearing next week after losing an appeal over a match manipulation case from 2008.
French side Olympique Lyonnais were given a tricky tie against Spain's Real Sociedad, while former champions Celtic of Scotland will face a long journey to Central Asia after they were drawn against the Kazakhstan champions Shakhter Karangandy.
Celtic, winners in 1967, will have to travel around 5,500 kilometres and across five time zones for the first leg on Aug 20 or 21.
Shakhter are attempting to become the first side from Kazakhstan to reach the group stage since the country's federation moved to UEFA from the Asian Football Confederation in 2002.
Milan, who finished third in Serie A last season, were given the tie they probably dreaded most against the 1988 European champions, even though Dutch clubs are no longer the force they used to be in European club football.
The tie is a repeat of the 2005 semi-final which Milan won on away goals after a 3-3 aggregate draw where Phillip Cocu, the current PSV coach, scored twice as PSV won the second leg 3-1.
Massimiliano Allegri's team will not have played a competitive fixture before they visit the Netherlands for the first leg.
They could also be without forward Mario Balotelli, who limped out of a pre-season friendly against Los Angeles Galaxy on Wednesday with a thigh muscle problem.
Only two Italian teams qualify directly for the group stage after Serie A dropped below the Bundesliga in UEFA's complex system of coefficients.
Arsenal, who are attempting to reach the last 16 for the 14th season in a row, will travel to Istanbul for the first leg of their tie.
Fenerbahce were banned from European competition for two years over a domestic match-fixing case but reinstated pending an appeal at the Court of Arbitration for Sport (CAS).
UEFA has not said what will happen if Fenerbahce, who beat Salzburg in the third qualifying round, beat Arsenal but then lost their case at CAS.
CAS has said it will announce its decision in the case "before August 28", the same week the second legs are due to be played.
Kharkiv face a UEFA disciplinary hearing on Tuesday after losing an appeal at CAS over a match manipulation case dating back to 2008.
"Kharkiv is a good draw. Ukrainian teams are tough ones but I look forward to the match in my birth country," said Schalke midfielder Roman Neustaedter.
In other ties, former semi-finalists Austria Vienna, aiming to become the first team from their country to qualify for seven years, were paired with Croatian champions Dinamo Zagreb.
Portuguese surprise package Pacos de Ferreira take on ambitious Russians Zenit St Petersburg and Steaua Bucharest, the other former winners in Friday's draw, play Legia Warsaw.
The 10 winners of the playoff ties will join 22 teams from Europe's top leagues who qualified directly for the group stage.
(Additional reporting by Karolos Grohmann; Writing by Brian Homewood; Editing by Ossian Shine/Patrick Johnston/Pritha Sarkar)
