The 26-year-old Iran international has informed the Bundesliga strugglers that he will not be extending his contract, which expires at the end of June.
It is not yet known where Davari will be plying his trade next, but there is unlikely to be a shortage of suitors for a player who has become a key member of promoted Braunschweig's side this season this term.
He started the campaign on the bench as second choice behind Marjan Petkovic, but has not missed a game since forcing his way into the first team in the eighth round of matches.
Davari joined Braunschweig from Mainz in 2009 and has made a total of 87 appearances for them, most of which came in second division, although he made his debut for the club in the third division in 2010.
Braunschweig are currently bottom of the Bundesliga standings with 25 points but are just two points adrift of safety and have won two of their last three.