He finished third in the 100m at last month's Pan Pacific championships in his homeland then withdrew from the 50m sprint and was told by doctors to rest his back and avoid flying until it was healed.
"I am very disappointed to not be able to compete," Magnussen said in a statement.
The inaugural Singapore Swim Stars features some of the sport's most accomplished stars, who will be racing for cash prizes rather than medals.
(Reporting by Julian Linden; editing by Amlan Chakraborty)
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