The 22-year-old started just 10 league matches in a campaign afflicted by a litany of fitness problems and also a lengthy illness.
The decision to have an operation on a persistent groin problem has come after his club secured a third successive league title but has ruled Forrest out of Scotland's friendly match with Nigeria this month.
"Jamesie will not be going away with Scotland for their game at Craven Cottage at the end of this month," said Neil Lennon, the Celtic manager. "He has had surgery on his groin and needs a bit of time to recover.
"I don't know if Nir Biton will be going away with Israel. But we hope they can both come back for the start of our pre-season."
By that time Lennon will hope to have refined his squad ahead of a new campaign. He knows already most of the clubs which Celtic could face in the second qualifying round of the Champions League - with the likes of Malmo, Dinamo Tbilisi and St Patrick's among the clubs which could be drawn with the Scottish champions - although UEFA have still to confirm whether or not they will regionalise the draws again.
It is not yet known where Heerenveen striker Alfred Finnbogason will be playing either, although the Celtic signing target is keen to leave the Dutch club. "I will listen to every club who comes to an agreement with Heerenveen," he said.