The group - made up of Zayn Malik, 19, Harry Styles, 18, Niall Horan, 19, Louis Tomlinson, 20, and 19-year-old Liam Payne - will embark on an eight-month run of shows in December, and bosses are concerned they are not as fit as they need to be to undertake the gruelling schedule.
A source told the Daily Mirror newspaper: "We're concerned about them - and Liam is still healing after he broke his toe when he MacBook fell on it this summer in the US.
"Zayn and Niall have both been on crutches so now they're all on hardcore fitness regimes."
Niall has dislocated his knee a total of 14 times, while Harry was this year forced to take up pilates to deal with bad posture brought on from his high school paper-round.
However, the group are looking forward to the throngs of screaming girls who will accompany them on their tour.
Niall said recently: "I love it. I love the screaming. They love it, too: they're all got their tickets and they've been waiting a year or so to see you, so you've got to give it your best."