Cristiano Ronaldo sent the Red Devils 1-0 ahead in the 13th minute of the contest, but Young Boys levelled the scores in the 66th minute through Moumi Ngamaleu before Theoson-Jordan Siebatcheu scored the winner for the home side in the 95th minute.
Solskjaer has now suffered seven defeats in 11 Champions League matches, with the club losing each of their last three in the competition against Paris Saint-Germain, RB Leipzig and Young Boys.
Man United's last victory in the European Cup was a 4-1 home success over Istanbul Basaksehir last November, while Solskjaer has also overseen wins over Leipzig and Paris Saint-Germain (on two occasions).
The defeat has already left the 20-time English champions playing catch-up in Group F, and there will be pressure on the team to pick up a result in their next European fixture at home to Villarreal on September 29.
The Red Devils currently sit top of the Premier League table, though, and will be looking to continue their strong domestic form when they travel to West Ham United on Sunday afternoon.
CSKA Moscow 
FC Rostov 
Leicester 
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Valencia 
Betis 
Dynamo Kyiv 
Chornomorets Odesa 
Verona 
Inter 
Bayer Leverkusen 
FC Heidenheim 
Borussia Dortmund 
SC Freiburg 
VFL Wolfsburg 
Union Berlin 
Arsenal 
Nottingham Forest 
Everton 
Brentford 
Spartak Moscow 
Lokomotiv Moscow 
Rangers 
Dundee Utd 
Atletico Madrid 
Alaves 
Lens 
Marseille 
Ingulets Petrove 
Shakhtar Donetsk 
AC Milan 
Juventus 
ST Malo 
Bordeaux 
Manchester City 
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Werder Bremen 
Girona 
Espanyol 
Feyenoord 
Heerenveen 
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Grenoble Foot 38 
Heart Of Midlothian 
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Reims 
Lyon 
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Celta Vigo 
Barcelona 
Benfica 
Estrela Da Amadora 
Sparta Rotterdam 
AZ Alkmaar 
Southampton 
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