Spaniard Marquez suffered a dislocated shoulder while training at home earlier in the season, and it has popped out on several occasions since then – most notably during qualifying in Valencia.
Despite suffering with the injury, Marquez was able to win a fifth MotoGP title in 2018 but will now have a procedure to treat the issue.
Three-time champion Lorenzo, who is replacing retired compatriot Dani Pedrosa for Honda on the grid next year, fractured his football at Aragon in September and had surgery on Monday.
Both riders will now be looking to regain full fitness ahead of the Sepang Test weekend, which begins on February 6.
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