The Dons' six potential opponents in the regionalised draw included Dundalk and Belfast-based Crusaders but they were paired with opponents from further afield.
The opening tie is scheduled to take place at Pittodrie on July 3 with the return leg a week later, although the final details are yet to be confirmed.
Aberdeen played in the Latvian capital 20 years ago in the UEFA Cup but were on the end of a shock exit at the hands of Skonto Riga in the second preliminary round, going out on away goals following a 1-1 draw at Pittodrie.
Daugava currently sit seventh in the 10-team Latvian league, 20 points behind leaders Skonto with 17 games played. They moved to the capital in 2012 after changing their name from FK Jurmala.
Unseeded Daugava recently announced the signing of two former Liverpool reserves - Senegalese left-back Emmanuel Mendy and Brazilian striker Vitor Flora.
Aberdeen will play Dutch side Groningen if they get through.
St Johnstone have been handed a game against Swiss side Lucerne in the second qualifying round, while seeded Motherwell will play the winners of the tie between Bangor and Stjarnan.
In the first round, Linfield were handed a tie against Faroese side B36 Torshavn while Derry City face Aberystwyth Town. Linfield will face AIK of Stockholm if they beat their Faroese opposition and Dundalk have the incentive of a second-round clash with Hajduk Split.
Crusaders take on Ekranas of Lithuania while Glenavon take on FH Hafnarfjordur of Iceland.
Welsh seeds Bangor City have been given a tough game against Icelandic league leaders Stjarnan while Airbus UK Broughton take on Norwegian side FK Haugesund.
Sligo Rovers play Lithuanians FK Banga while Dundalk face Jeunesse Esch of Luxembourg.