The Port Adelaide captain left the ground late in Sunday's match against the GWS Giants after attempting to tackle opponent Toby Greene.
The club confirmed he had dislocated a finger after the match.
High performance manager Darren Burgess confirmed Boak underwent surgery on Monday evening and will miss games against both Sydney and Collingwood.
"Travis has dislocated his finger with minor ligament damage," Burgess told portadelaidefc.com.au.
"He had scans and then surgery today and will miss the next two weeks."
Port Adelaide will play Sydney at AAMI Stadium on Saturday at 1:10pm with the final team to be confirmed on Thursday night.
