The matches will be played in February and March next year.
Real Madrid will play Liverpool in the last 16 of this season's Champions League -- a repeat of May's final in the French capital Paris.
The Spanish champions beat Jurgen Klopp's men 1-0 to lift the trophy and Monday's draw has again pitted them against each other.
The draw's other standout tie is Paris Saint‑Germain versus Bayern Munich, two giants of European football who contested the 2020 final.
PSG was unseeded in this draw after a stoppage-time goal for Benfica in a 6-1 win last week at Maccabi Haifa meant the Portuguese club topped their group.
Benfica was rewarded on Monday with a pairing against Belgian side, Club Brugge.
The lowest-ranked team, AC Milan, will be at home against Tottenham in the first leg in its return to the Champions League knockout rounds after a nine-year absence.
Manchester City was paired with Leipzig, and Chelsea was drawn to face Borussia Dortmund in two Premier League vs. Bundesliga clashes.
Napoli -- the top-scoring team in the group stage -- will play Eintracht Frankfurt, while Inter Milan faces Porto.
Champions League draw - last 16
- RB Leipzig vs Manchester City
- Club Brugge vs Benfica
- Liverpool vs Real Madrid
- AC Milan vs Tottenham
- Eintracht Frankfurt vs Napoli
- Borussia Dortmund vs Chelsea
- Inter Milan vs Porto
- Paris Saint‑Germain vs Bayern Munich
First-leg games are played from 14-22 February. Return games are from 7-15 March.
The unusually long wait of more than three months between the group and knockout stages was caused by the World Cup in Qatar being played in November and December.
The congested season meant the six-round group stage started earlier than usual in September and was completed in just nine weeks.
Who is playing who in the Europa League?
Meanwhile, Manchester United will play Barcelona in the knockout round play-off of the UEFA Europa League.
The Spanish giants enter Europe's second-tier club competition after being knocked out of the UEFA Champions League group stage.
Elsewhere, Juventus were drawn against Nantes, and Ukrainian side Shakhtar Donetsk will play another French side, Rennes.
Sevilla, who have won the competition a record six times, will take on Dutch side PSV Eindhoven.
Teams who win their knockout round ties will progress to the Round of 16. This season's Europa League final will take place in Budapest on May 31.
Europa League draw - knockout round
- Barcelona vs Manchester United
- Juventus vs Nantes
- Sporting CP vs Midtjylland
- Shakhtar Donetsk vs Rennes
- Ajax vs Union Berlin
- Bayer Leverkusen vs Monaco
- Sevilla vs PSV Eindhoven
- Salzburg vs Roma