The Clarets defender has been granted compassionate leave to return to his native Canada as his fiancee is due to give birth this week.
Burnley manager Sean Dyche said: "David asked if he could go home and I have absolutely no issue with that because family always comes first."
Edgar, 25, will now return to pre-season training in late June, following his expected summer involvement in Canada's CONCACAF Gold Cup fixtures.
The player's absence opens up another slot for Dyche to give game time to a youngster, with an eye on next season after the weekend win at Wolves secured Burnley's Championship status.
He told the club's official website: "Blooding a few youngsters is in my thoughts. I was looking at that seven games ago but, due to the madness of this division, never had the chance.
"But we have to see what's available for next season and we have got contract situations (to resolve) that have been there all year.
"That's been a tough challenge to keep the players motivated and stimulated to play for this club while they are looking over their shoulders and what-ifs.
"But we will definitely look at some of those younger players now, and whether they are on the bench or not they will be in and around it somewhere."
First-team regulars Lee Grant, Michael Duff, Chris McCann, Dean Marney and Martin Paterson are out of contract next month.