The date of the away and home legs will be confirmed in due course, but City will play the first leg away.
The Blues have never met FC Basel competitively.
City Director of Football Txiki Begiristain said: "We have to respect FC Basel and we have to be careful.
"We need to be ready to play them and do our best because obviously we want to go as far as we can in this competition
"We showed against Napoli that we can do well home or away. We had to fight to qualify and to win the group and I think we've shown the character and personality needed to do well in the Champions League."
FC Basel finished runners-up to Manchester United in Group A, ending above CSKA Moscow and Benfica.
The Swiss side beat the Reds 1-0 in Basel but lost 3-0 at Old Trafford as well as losing at home to CSKA.
They play their home games at St Jakob Park which holds approximately 38,000 fans.
Basel are currently second to Young Boys in the Swiss Super League.
When will the games be played?
The first leg will be in Basel on February 13 and the return leg at the Etihad will be on 7 March.
Juventus v Tottenham
Basel v Man City
Porto v Liverpool,
Sevilla v Man Utd
Real Madrid v Paris St-Germain,
Shakhtar v Roma
Chelsea v Barcelona, Bayern v Besiktas
Champions League - key dates:
16 March: Quarter-final draw
3/4 April: Quarter-finals, first leg/ 10/11 April: Quarter-finals, second leg
13 April: Semi-final and final draw
24/25 April: Semi-finals, first leg/ 1/2 May: Semi-finals, second leg
26 May: Final (NSK Olimpiyski, Kyiv)
Away Tickets and Transport
Fans wanting to watch FC Basel v City away in Switzerland on Tuesday 13 February in the last 16 of the UEFA Champions League can register their interest now for a Thomas Cook Sport day trip.
The Club’s Official Supporter Travel Provider will be providing a return flight from Manchester and transfers to and from St. Jakob-Park for £269 per person.
Please note match tickets must be purchased directly from the club when they go on sale, and places on the trip will only be confirmed once the match ticket has been purchased.