Ronny Deila’s side, who won the Scottish Premiership ahead of Aberdeen, will begin their campaign on July 14 or 15 with the second leg a week later on July 21 or 22.
Celtic, who beat Icelandic side KR Reykjavik 5-0 on aggregate at the same stage last year, were drawn out first so are scheduled to be at home in the first leg.
Despite overcoming KR Reykjavik, the Hoops failed to reach the group stage of the Champions League last season when they lost out to Slovenian side Maribor having been re-instated into the play-off round even though they suffered a 6-1 aggregate defeat by Legia Warsaw, with the Polish side ejected from the competition by UEFA for fielding an ineligible player.
Stjarnan defeated Motherwell and Lech Poznan – the eventual champions of Poland – in the Europa League qualifying rounds last season before being hammered 9-0 on aggregate by Inter Milan in the play-off for the group stage.
They won their first Icelandic league title in dramatic style in October, converting a stoppage-time penalty in their final game to beat FH 2-1 and finish one point ahead of their opponents.
Irish club Dundalk face a tough test against BATE Borisov, the champions of Belarus, in the second qualifying round.
Elsewhere in the first qualifying round, The New Saints of Wales, one of the seeded teams, will play B36 Torshavn of the Faroe Islands, while Northern Ireland side Crusaders were drawn against Estonian side Levadia Talinn.
Champions League qualifying draw:
Lincoln Red Imps v Santa Coloma
Pyunik v Folgore/Falciano
Crusaders v Levadia Tallinn
B36 Torshavn v The New Saints FC
Ties to be played June 30/July 1 and July 7/8
Hibernians v Maccabi Tel-Aviv
Apoel Nicosia v Vardar
FK Karabakh v Rudar Pljevlja
FK Sarajevo v Lech Poznan
Maribor v Astana
BATE v Dundalk
HJK Helsinki v FK Ventspils
FC Midtjylland v Lincoln Red Imps/Santa Coloma
Molde v Pyunik/Folgore/Falciano
Malmo FF v FK Zalgiris Vilnius
Celtic v Stjarnan
AS Trencin v Steaua Bucuresti
Partizan Belgrade v Dila Gori
Ludogorets v Milsami
CS Fola Esch v Dinamo Zagreb
Skenderbeu v Crusaders/Levadia Tallinn
B36 Torshavn/The New Saints FC v Videoton FC
Ties to be played July 14/15 and July 21/22