The 27-year-old had the immediate procedure after standard pre-season tests indicated a potential risk.
Pompey, preparing for a return to English football's second-tier Championship, have not said when Bishop might return to action.
"Definitely not the start to the season I expected, receiving this news," Bishop the club's website on Tuesday.
"It's been a really uncertain time for myself, my wife and new baby. Despite the difficult circumstance, I am extremely grateful to have been referred to a world-leading expert in a ground-breaking procedure to get me back to full fitness.
"I would like to thank everyone at Portsmouth Football Club for their ongoing support throughout.
"I look forward to playing in front of you all at Fratton Park on my return."
Bishop, who joined south coast side Portsmouth from Accrington in 2022, scored 21 goals in 48 games last season as the club won the League One title.
He has not featured in any of Portsmouth's pre-season games ahead of their Championship opener away to Leeds on August 10th.
The club added in a statement: "Everyone at Portsmouth FC is fully supportive of Colby and his family."
