The 29-year-old suffered the injury during the 2-0 defeat to Chesterfield on January 25 and has not played a part in the two games since.
Boss Andy Hessenthaler has refused to put a time-frame on the player's recovery, amid fears he could lose part of his finger by playing on.
"He had his op on Tuesday and it's all gone well," Hessenthaler told Kent Online.
"We can only go by the consultants now whether Danny will be involved again (this season). I really can't comment on time.
"All I know is that he texted me to wish all the boys the best on Tuesday and said to me the operation was a success. Let's hope we can get him back as quick as we can."
Source: PA
Source: PA