Proschwitz, 27, will join up with the club in Dublin ahead of Friday night's friendly against Dundalk.
The German has struggled to hold down a regular place in Hull's starting line-up since arriving from SC Paderhoen 07 in the summer of 2012.
He has made six appearances for Steve Bruce's side this season, scoring two goals.
Hull paid B£2.5million to bring Proschwitz to England, but he has made only five starts for the club, having been used mainly off the substitutes' bench.
He has made a total of 27 appearances for the Tigers and has scored seven goals for the club.