Daniela and twin sister Sandra (fellow pro-player) were born in Vienna, Austria.

Daniela played doubles with sister Sandra on the WTA Tour and the ITF Women's Circuit.

Daniela played her final professional match on 14 December 2006 in Valašské Meziříčí, Czech Republic, partnering sister Sandra and losing in round one against Eva Hrdinová and Stanislava Hrozenská, 5–7, 2–6.

In January 2007, both Klemenschits twins were diagnosed with a rare form of abdominal cancer, squamous cell carcinoma, forcing their retirement.

[1] Fellow tennis players rallied for Klemenschits and donated money to pay for the removal of several tumours and the expensive medical care required.