Boak suffered the injury in the final minutes of Sunday's 75-point win over Greater Western Sydney at Skoda Stadium.
Along with the dislocation, scans also found minor ligament damage, according to portadelaidefc.com.au.
On Monday night, Boak posted a photo of his injured finger on social networking site Instagram (below), writing: "Not the best looking finger, just didn't want to go back in. Surgery went well. Will be back very soon."
Boak will miss matches against the Sydney Swans and Collingwood, before an expected return against Essendon in round 15.
The 24-year-old has played every game this season, averaging 25.1 disposals and 4.2 tackles per outing.
