The defender has been recovering from a thigh injury and Sir Alex Ferguson said: "He got an injury on the Wednesday and, straight away, we decided to have the operation, so he's out. It's difficult to say with a metatarsal but it could be ten weeks. He's not carrying any luck, the kid, but he's young and we've done the right thing in getting it done immediately and getting him back on the road as quickly as we can."
Smalling's absence is a further blow to United's hopes of claiming a 20th title, which Ferguson has made the club's priority. Jonny Evans is already a doubt for the opening league fixture at Everton on 20 August, though Nemanja Vidic, the captain, is expected to be available following his knee injury.
United could manage only a draw against Ajax, with Bébé's added-time equaliser cancelling out the 86th-minute opener from Alcardo van Graan's flicked-heel finish.
Kagawa had made a first start in United colours and shown a touch, vision and ability to mould play from the hole position in a 4-4-1-1 that suggests his £12m fee from Borussia Dortmund could be a shrewd investment.
As Ajax have never been champions of South Africa they were not the ideal barometer of the forward's abilities. But the Japanese was United's classiest operator throughout, wandering into space behind Javier Hernández, the main striker, to cause problems and fashion chances for the Mexican.
One came a minute after the break when Kagawa dropped into midfield, peered up, then slid the ball on the diagonal into Hernández's run, though the striker steered the chance wide.
The 24-year-old had spurned an earlier opportunity when from a Scott Wootton cross from the right Hernández's header was saved by Sander Westerveld, the former Liverpool goalkeeper.
Kagawa missed as good an opportunity on the hour. This time, Hernández did the creating by flipping in a cross from the left and the 22-year-old headed down but wide of the right post.
Kagawa's afternoon ended on 77 minutes, and there was a subsequent flash of promise from Nick Powell, the £4m buy from Crewe Alexandra. Making his debut as a substitute, the 18-year-old produced a sharp save from the Ajax keeper Sean Roberts, with a fierce shot.
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