The Tigers opted for surgery after Fagan failed to respond to physiotherapy and injections.
Meanwhile, fellow striker Caleb Folan has undergone exploratory surgery on a knee problem.
The 28-year-old picked up in the 1-1 draw with Barnsley on 30 October.
The Hull club website said the operation produced results that were "very positive" but it is not yet know how long Folan will be on the sidelines for.
Source: BBC Sport
Source: BBC Sport