All qualifying ties are being played as single-leg encounters behind closed doors on 17 September.
Meanwhile, Motherwell visit Northern Ireland side Coleraine, while Rangers will travel to Gibraltar to play against Lincoln Red Imps.
Aberdeen are away to Viking of Norway, while Republic of Ireland side Shamrock Rovers host Italian giants AC Milan.
Welsh side Bala Town have been drawn at home to 10-time Belgian champions Standard Liege.
The one-off ties will go to extra time and a penalty shootout if required.
Following their early exit from Champions League qualifying, Celtic will enter the Europa League in the third qualifying round.
After the play-off round, FA Cup winners Arsenal and fifth-placed Premier League side Leicester City will enter at the group stage.
Second qualifying round ties involving British & Irish sides:
Inter Escaldes v DUNDALK
LINFIELD v Floriana
CONNAH’S QUAY NOMADS v Dinamo Tbilisi
B36 Torshavn v THE NEW SAINTS
COLERAINE v MOTHERWELL
Viking v ABERDEEN
BALA TOWN v Standard Liege
Lokomotiv Plovdiv v TOTTENHAM HOTSPUR
Lincoln Red Imps v RANGERS
SHAMROCK ROVERS v AC Milan
