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.
Jockey William Buick will be sidelined for at least six weeks after being injured in a fall in the United States.