United defender Rio Ferdinand tweeted: "Landed in Germany....just....I've only just recovered after that choppy landing! #TouchedCloth!!"
The team, who play Bayer Leverkusen on Wednesday night in a key Champions League clash, was about to land at Cologne-Bonn airport when the touch-down was aborted.
Just 400 metres or so above the runway, the pilot pulled the nose of the plane up again - due to another incoming plane, initial reports suggested.
The team then landed safely and went to their hotel to prepare for Wednesday's showdown.
United top Group A with eight points, just one ahead of hosts Leverkusen, and need to beat Sami Hyypia's Bayer to confirm their place in the knock-out stages.
Manchester's manager David Moyes defended Wayne Rooney after he was given a yellow card for kicking Jordon Mutch during Sunday's disappointing 2-2 Premier League draw at Cardiff City.
"His form, attitude and temperament have been first class this season, I can't fault it," said Moyes, with Rooney having scored eight goals so far this season in Europe and the Premier League.
"Players sometimes have their moments when they flare up, but I want Wayne to have a fire in his belly, I want him to be tough and aggressive.
"I don't want him kicking anyone, but we are seeing a Wayne Rooney who is in top form and scoring goals.
Moyes said United were eager to win their last away group game to wrap up their place in the knock-out phase before their final group match at home to Shakhtar Donetsk in a fortnight.
Bayer are unbeaten at home since losing 2-1 at home to European champions Bayern Munich in March and Moyes is wary of Hyypia's side, who are second only to Bayern in the Bundesliga.
"The group is very open and we have a big job to do here in Germany," said the Scotsman.
"We want to try and get the job done, we know we have a hard game against Leverkusen, we want to avoid things being decided by that last game."
Centre-back Nemanja Vidic is ruled out with concussion, while striker Robin van Persie is recovering from a groin injury.
Eight Manchester United players and three club officials died in what became known as the Munich air disaster in 1958 when their plane crashed, killing 23 people.