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Urban had the procedure on Wednesday, and he will not be able to speak for three weeks, spokesman Paul Freundlich told Reuters. The singer is recovering at an undisclosed location.
One day ahead of the procedure, Urban posted a video on his website thanking fans for their support.
"I want to thank you for sending such good wishes for my upcoming surgery," Urban said. "I can't express enough my gratitude to you guys; it feels like family."
He said he had received cards, gifts, emails, flowers and a large basket of items he would need as he recuperates including hand-written notes to hold up when he needs something.
Urban, whose hits include "Long Hot Summer" and "You Look Good in my Shirt," announced earlier in November that he was postponing several shows while he sought medical care.
The polyp developed during his recent "Get Closer World Tour 2011," and in Monday's video Urban took note of the fans who had turned out to see him perform during what he called his "crazy great phenomenal year.
"The tour was incredible for me, and seeing you guys sing along with my new songs was heartening for me. Personally I had an incredibly great time and I was sad to see it end," he said.
Urban is not the only singer to have problems with his vocal cords. In the past month, British pop singer Adele had similar surgery as did Kiss frontman Paul Stanley.