The 24-year-old, who will be gunning for a third successive gold in the blue riband event in Russia in August, was given the advice by a consultant after tearing a muscle under his left shoulder blade.
His coach Mitch Falvey told the newspaper Magnussen would probably be forced to skip Mare Nostrum races in Canet-en-Roussillon and Monaco next month.
"Anything he does at racing intensity aggravates it," he said.
Magnussen, who won the world title in Shanghai in 2011 and successfully defended it in Barcelona two years later, missed out on gold in the London Olympics by the length of a finger, pipped at the wall by American Nathan Adrian.
His compatriot Emily Seebohm, the 100m backstroke silver medallist in London and Barcelona, also suffered a setback to her preparations for the world championships this week.
The 22-year-old, who swam the best time of the year in the 100m backstroke (58.89 seconds) in January, posted a picture of herself on crutches with her right knee encased in a brace on Twitter.
"Bad news dislocated my knee cap good news no major damage! Back in the pool soon and back to my prep!" she wrote on Tuesday.
(Reporting by Nick Mulvenney, editing by Julian Linden)
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