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The 2022 Wimbledon runner-up was left "devastated" after being forced to withdraw from the Australian Open on home soil last week.
Kyrgios was ruled out of his home grand slam after an MRI scan on his knee revealed a cyst as a result of a small lateral meniscus tear.
He went under the knife on Monday and is now battling to be ready in time for the first Masters 1000 event of the season at Indian Wells, which starts on March 6.
"The surgery was a great success," Horsfall said.
"We couldn't have been more pleased with the outcome of it. Now we will be pushing ahead for a speedy recovery and are aiming to see everyone at Indian Wells."
Kyrgios won the seventh ATP Tour singles title of his career in Washington last August and claimed the Australian Open men's doubles title with Thanasi Kokkinakis 12 months ago.
The 27-year-old, who has yet to play competitively this season, is a two-time quarter-finalist on the hard courts at Indian Wells.