Context. SN2011fe was detected by the Palomar Transient Factory in M101 on August 24, 2011, a few hours after the explosion. From the early optical spectra it was immediately realized that it was a Type Ia supernova, thus making this event the brightest one discovered in the past twenty years. Aims. The distance of the event offered the rare opportunity of performing a detailed observation with the instruments onboard INTEGRAL to detect the γ-ray emission expected from the decay chains of 56 Ni. The observations were performed in two runs, one before and around the optical maximum, aimed to detect the early emission from the decay of 56 Ni, and another after this maximum aimed to detect the emission of 56 Co. Methods. The observations performed with the instruments onboard INTEGRAL (SPI, IBIS/ISGRI, JEMX, and OMC) were analyzed and compared with the existing models of γ-ray emission from this kind of supernova. In this paper, the analysis of the γ-ray emission has been restricted to the first epoch. Results. SPI and IBIS/ISGRI only provide upper limits to the expected emission due to the decay of 56 Ni. These upper limits on the gamma-ray flux are 7.1 × 10 −5 ph/s/cm 2 for the 158 keV line and 2.3 × 10 −4 ph/s/cm 2 for the 812 keV line. These bounds allow rejecting at the 2σ level explosions involving a massive white dwarf, ∼1 M in the sub-Chandrasekhar scenario and specifically all models that would have substantial amounts of radioactive 56 Ni in the outer layers of the exploding star responsible for the SN2011fe event. The optical light curve obtained with the OMC camera also suggests that SN2011fe was the outcome of the explosion of a CO white dwarf, possibly through the delayed detonation mode, although other ones are possible, of a CO that synthesized ∼0.55 M of 56 Ni. For this specific model, INTEGRAL would have only been able to detect this early γ-ray emission if the supernova had occurred at a distance < ∼ 2 Mpc. Conclusions. The detection of the early γ-ray emission of 56 Ni is difficult, and it can only be achieved with INTEGRAL if the distance of the event is close enough. The exact distance depends on the specific SNIa subtype. The broadness and rapid rise of the lines are probably at the origin of this difficulty.