The opening tie is scheduled to take place at Pittodrie on 3 July with the return leg a week later, although the final details are yet to be confirmed.
Aberdeen manager Derek McInnes admitted to having little knowledge of his opening-round rivals but is expecting a tough battle to reach round two.
"They are well into their season, having already played 17 matches," he told Sky Sports News.
"They finished fourth last year and are currently sitting seventh in the league this time around. The difficulty we will have is because we are in the middle of pre-season while they have the game-time advantage.
"But it's up to us to make sure we are ready for the game. It's a draw that's not too difficult to travel to and one we are all excited about as we want to do as well in it as we can."
Should Aberdeen successfully negotiate Daugava they will be paired with Dutch side FC Groningen in the second qualifying round.
Motherwell, who finished runners-up to Celtic in the Premiership last season, come in at that stage where they face either Stjarnan of Iceland or Bangor City while Scottish Cup winners St Johnstone travel to Switzerland to play FC Luzern.
UEFA Europa League first qualifying round draw (British and Irish teams):
B36 v Linfield
Derry City v Aberystwyth
Aberdeen v Daugava Riga
Crusaders v FK Ekranas
Stjarnan v Bangor City
Jeunesse Esch v Dundalk
FH Hafnarfjordur v Glenavon
Banga v Sligo Rovers
FK Haugesund v AUK Broughton FC
FC Vaduz v College Europa FC
Ties to be played 3 and 10 July
UEFA Europa League second qualifying round draw (British and Irish teams):
Neman Grodno v FH Hafnarfjordur/Glenavon
Motherwell v Stjarnan/Bangor
Crusaders/ Ekranas v Vaasa/Brommapojkarna
Aberdeen/Daugava Riga v Groningen
B36/Linfield v AIK Solna
Luzern v St Johnstone
Rosenborg/ Jelgava v Banga/Sligo Rovers
Sarajevo v Haugesund/AUK Broughton
Derry/Aberystwyth v Soligorsk
Chorzow v Vaduz/College Europa
Hajduk Split v Jeunesse Esch/Dundalk
Ties to be played 17 and 24 July