He was unseated as Royal Ascot winner Permian was fatally injured after coming last in the Secretariat Stakes at Arlington on 12 August.
Buick, 29, suffered a compression of his T12 vertebrae and he will be assessed again in six weeks.
"I have plenty of respect for the injury and I realise how lucky I have been," he said.
Buick is one of the leading jockeys in Britain, and a retained rider for Sheikh Mohammed's Godolphin team.
Permian, trained by Mark Johnston, suffered a broken leg and was put down.

The 22-year-old Australian will act as cover at Allianz Park during the Rugby World Cup, which takes place between 18 September and 31 October.
Sarries could potentially lose Jamie George and Schalk Brits to England and South Africa duty at the tournament.
"We felt we that we needed some more depth in the hooking position," Sarries director of rugby Mark McCall said.
"Alongside Scott Spurling and Jared Saunders, Dave will provide us with more options.
"He has been training with us since we've returned to pre-season and has fitted into the club very well."
Porecki has had a spell with Super Rugby outfit Waratahs and has been playing for Sydney side Manly Marlins.
Saracens will begin the defence of their Premiership title at home to Sale Sharks on Saturday, 17 October.

The British Speedway Promoters' Association, whose chairman Keith Chapman has been involved in negotiations to keep the club going, say an agreement has been reached.
It has also been announced that a 15-year lease has been signed for the team's Beaumont Park venue.
"Hopefully this is a new start for the club and it will have a good future," Chapman told BBC Radio Leicester.
"Further meetings are now necessary to establish the management structure of the club, a racenight for the 2017 season and other arrangements," said a Leicester Speedway statement.
Jockey William Buick will be sidelined for at least six weeks after being injured in a fall in the United States.
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Premiership champions Saracens have signed hooker Dave Porecki on a short-term contract.
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Leicester Lions' future has been secured following financial problems.