8 pages, 3 figuresInternational audienceThe massive binary system Eta Carinae and the surrounding HII complex, the Carina Nebula, are potential particle acceleration sites from which very-high-energy (VHE; E > 100 GeV) \gamma-ray emission could be expected. This paper presents data collected during VHE \gamma-ray observations with the H.E.S.S. telescope array from 2004 to 2010, which cover a full orbit of Eta Carinae. In the 33.1-hour data set no hint of significant \gamma-ray emission from Eta Carinae has been found and an upper limit on the \gamma-ray flux of 7.7 x 10-13 ph cm-2 s-1 (99% confidence level) is derived above the energy threshold of 470 GeV. Together with the detection of high-energy (HE; 0.1 GeV > E > 100 GeV) \gamma-ray emi...