The Bombers agreed to release the veteran for a fortnight when a new contract was negotiated ahead of the season.
It’s believed Hille, 31, departed Melbourne for France on Sunday.
Paddy Ryder is due to return to the side for Friday night's blockbuster against Geelong at Etihad Stadium.
"When David signed a one year contract extension with the club at the start of this season, he flagged that this trip was a possibility," Essendon football manager Danny Corcoran told the club's website.
"He has had a long standing family commitment overseas that the club agreed he would be able to honour.
"David has been a valuable contributor to the team this season in the absence of Paddy Ryder who has been missing through suspension, and we now look forward to him being available for selection again in two weeks time."
Former Essendon captain Matthew Lloyd was surprised by the move.
"It is staggering in regards to him, probably in his last year of his career, playing for his career," Lloyd told Channel 9.
"I saw him grab at his hamstring in the last two minutes of the game (against GWS) - I'm wondering if it's a last minute decision or if it has been in plan for a long period of time," Lloyd speculated.
Hille will miss Essendon's round eight game against the Brisbane Lions, as well as the match against the Cats on Friday night.
Matt Thompson is a reporter for AFL Media. Follow him on Twitter @MattThompsonAFL
