The second legs will be played a week later, on Thursday, 5 July.
The Lakesiders will be competing in the Europa League for a fifth season while Druids have reached Europe for only the second time in their history.
Bala will play their home leg at Rhyl's Belle Vue while Druids will use New Saints' Park Hall in Oswestry.
"We've got a few people within the club that are scouring the internet to try and find out a bit more information about them," Bala manager Colin Caton said of their opponents, who have won their national championship seven times.
"We'll contact the Welsh FA and they will give us a run down on them so we'll wait for the information off them, have a look at a lot of clips and videos, so some research and plan the best we can.
"They've done well in their own domestic league and are in Europe so obviously they're good. It's going to be difficult."
Welsh Cup winners Connah's Quay Nomads enter the competition at the first qualifying round stage.
The draw for the first qualifying round will be made on 20 June and the first leg held on Thursday, 12 July.
Welsh champions New Saints enter the Champions League at the first qualifying round.
Europa League preliminary round Europa (Gibraltar) v Prishtina (Kosovo)
Sant Juliŕ (Andorra) v Gżira (Malta)
Engordany (Andorra) v Folgore (San Marino)
B36 Tórshavn (Faroe Islands) v St Joseph's (Gibraltar)
Birkirkara (Malta) v KÍ Klaksvík (Faroe Islands)
Tre Fiori (Sand Marino) v Bala Town (Wales)
Cefn Druids (Wales) v Trakai (Lithuania)
- BBC |