Their Monarch Airlines airbus had dropped to a height of 400 metres as it prepared to land, when the plane suddenly took off again.
The pilot decided to abort the landing just 400m above ground— because another plane was on the runway just as they came in to land.
The chartered 185-seater Airbus 321 jet circled before landing safely at the second attempt, 10 minutes late at Cologne's Konrad Adenauer Airport on Tuesday.
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.
Rio Ferdinand tweeted: “Landed in Germany... just... I’ve only just recovered after that choppy landing.”
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.
United’s scare came a day after the death of Bill Foulkes, one of the survivors of the Munich tragedy which killed 23 passengers, including eight players, on their way home from a European Cup tie in Belgrade in 1958; Sir Bobby Charlton was not on the plane with the team.
Manchester United’s player will wear black armbands during their Champions League tie on Wednesday night as a mark of respect to Foulkes.
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.