This is a Military Sports Badge (Truppensportabzeichen), intended for wearing on the chest on a sports-shirt.
The Military Sports-Badge was introduced on October 22, 1932. It has the shape of a black shield with a vertical broad sword, similar to the Roman gladius, superimposed on it and pointing downwards.
The shield measures approximately 11 cm in width and 20,5 cm in height.
Not so easy to find early German military sportshirt insignia!
In clearly shirt removed good condition.