Their Monarch Airlines airbus had dropped to a height of 400 metres as it prepared to land, when the plane suddenly took off again.
Press Association Sport understands a number of passengers expressed their concern and, while a stewardess initially said there had not been a problem, the captain later came onto the speakers to confirm he had been forced to abort the landing as there was another plane on the runway.
United's entire first-team squad and coaching staff were on board ahead of Wednesday evening's Champions League fixture with Bayer Leverkusen.
However, neither Sir Alex Ferguson nor Sir Bobby Charlton, who on Monday paid tribute to fellow Munich survivor Bill Foulkes following his death, were travelling, even though they are both due to attend the game at the BayArena.
Other passengers were rather more graphic in their descriptions of the incident.
"That was not pleasant," said one. "Nobody really knew what was going on but everything seemed calm and then the plane suddenly took off again."
Thankfully, the aircraft eventually landed without further incident at 1740 local time.
It was not the ideal start to what manager David Moyes acknowledges is the "big job" ahead of his side as they seek to book a place in the last 16.
Sami Hyypia's men have been in outstanding form this season.
They are currently second in the Bundesliga and the only time they have failed to win at the Bay Arena was their draw with European Cup winners Bayern Munich last month.
Under the circumstances, it is little wonder Moyes believes the fixture represents the toughest United will face in their group campaign.
"We have a big job to do," he said. "Bayer Leverkusen have been in great form at home.
"My first feeling when I saw the group was that Shakhtar Donetsk away would be a real tough game. It did prove to be that way and we ended up with a draw there.
"But Leverkusen are in good shape in the group themselves. We know we are going to have a game on our hands."
United's problem stems from the fact they failed to overcome Real Sociedad three weeks ago.
That goalless draw in Spain represents the Basque outfit's only point in the entire competition.
So, should United fall to their first defeat in the competition tomorrow and Shakhtar win, it will set up a winner-takes-all confrontation with the Ukraine champions at Old Trafford in a fortnight.
It is not entirely a palatable prospect considering the uncertain form the Red Devils have been in.
That is why Moyes could even nurse a sense of relief on the flight back to Manchester if his side manage even a share of the spoils.
"We had a great opportunity in Sociedad to pull away further but we didn't take it," the Scot said.
"We want to try and get the work done as soon as we possibly can but if it has to go to the last game so be it."
Nevertheless, it is a pity Moyes should find his squad so stretched.
The former Everton boss was already aware he would be without Marouane Fellaini following the midfielder's red card in San Sebastian.
Michael Carrick's Achilles injury has robbed him of another senior player from his midfield ranks.
However, prior to the afternoon departure, he also had to strike a pen through the names of Nemanja Vidic and Robin van Persie.
Both men missed Sunday's draw at Cardiff, and Van Persie has not recovered from the combination of toe and groin complaints that have been plaguing him for a couple of months.
Vidic was able to train in the morning. Evidently, though, the Serbian is not fully over the concussion he suffered against Arsenal immediately prior to the international break.
"They are both injured," Moyes said. "Nemanja Vidic had concussion and Robin has a problem with his groin.
"Neither of them are long term but they are not quite ready yet."
That could mean they will be fit to face either Tottenham or Everton in the Premier League fixtures that immediately follow the German expedition.
Against Leverkusen, though, it could herald the immediate return of Phil Jones to central midfield after the groin injury he picked up on England duty a fortnight ago.
"Jones has travelled and is in the squad," Moyes said.
"It is normal to lose players to injury and suspension at big clubs.
"But we have a squad which we will be able to use and they can show what they can do."
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