And the Dutch side will have the option of making the move permanent at the end of the Eredivisie campaign.
The Australian international, who previously played in the Netherlands for Heracles, joined Town in June of last year after leaving West Bromwich Albion.
The 25-year-old made 30 appearances last season, but has not featured this time around.
Town boss David Wagner brought in fellow German Chris Lowe this summer, and the former Kaiserslautern man has been first pick.
Now Davidson, under contract at Town to 2018, will attempt to resurrect his career in Holland.
“This is a good move for everyone,” explained Wagner.
“Jason is a senior player and is obviously keen to play regular football and that is not something we can offer here at the moment.
“He has a profile in the Netherlands from his time playing in the country and we all wish him the best of luck.”
Melbourne-born Davidson, capped 22 times but not in the latest Socceroos squad, has also had a spell in Portugal.
He had three years in the Japanese football development system before playing first-team football for Aussie side Hume City at 17.
Groningen are two games into their league season and host Twente Enschede on Sunday.