With 15 minutes left to play in United's 3-2 Europa League win over Bodo/Glimt, the goalkeeper rushed out to clear the ball.
Jens Petter Hauge regained possession for the visitors at Old Trafford and tried to dribble around Onana as defenders ran back.
The United man was able to get a vital foot in with his challenge and prevent Bodo/Glimt from scoring as he was off his line.
However, replays appear to show his hand hitting the ball down onto the pitch, before he seemingly clawed it away from Hauge's feet, with the referee dismissing free-kick shouts in real time.
VAR conceded that Onana had handled the ball, but deemed it as accidental and allowed play to continue.
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But talkSPORT commentator Mark Wilson was left shocked by the decision, as he said: "We thought Andre Onana had made a brilliant sliding tackle, which in fairness he did.
"But he also used his hand to deny Hauge the chance to put the ball in the back of the net.
"Manchester United have got away with one there."
Former Sunderland left-back Michael Gray meanwhile stated on commentary: "This is incredible if he gets away with it, which it looks like he has."
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Onana avoided what could have been a sending off for United and fans on social media can't believe he stayed on the pitch.
Taking to X, one said: "Onana just stopped the ball with his hand 10 yards outside the box and nothing was done. That's a straight red."
"Blatant handball by Onana that bails him out there, no? How is that not a red?" a second asked.
A third said: "I'm kinda surprised Onana wasn't sent off for that handball."
"Onana has to be sent off surely??" added a fourth as United held on to win their second Europa League match of the season.
Alejandro Garnacho gave Ruben Amorim's side the lead inside the first minute following a goalkeeping error from Nikita Khaikin.
Bodo/Glimt then took the lead themselves thanks to two goals from Hakon Evjen and Philip Zinckernagel inside four minutes of play.
However, Rasmus Hojlund scored before the break to level the score before netting the winner inside five minutes of the second half.
It could have been a very different story though had Onana been punished for his handball late on in the match.
Full-time delivered a nervy first win for new head coach Amorim, who took to Old Trafford for the first time since his appointment.
United have risen to 12th in the Europa League league table and have sealed back-to-back wins in the competition.
They return to their iconic home on Sunday to welcome Everton in the Premier League, with the Amorim-era now off to winning ways.