Baryonic feedback effects lead to a suppression of the weak lensing angular power spectrum on small scales. The poorly constrained shape and amplitude of this suppression is an important source of uncertainties for upcoming cosmological weak-lensing surveys such as Euclid or LSST. In this first paper in a series of two, we use simulations to build a Euclidlike tomographic mock data-set for the cosmic shear power spectrum and the corresponding covariance matrix, which are both corrected for baryons following the baryonification method of Schneider et al. [1]. In addition, we develop an emulator to obtain fast predictions of the baryonic suppression effects, allowing us to perform a likelihood inference analysis for a standard ΛCDM cosmology with both cosmological and astrophysical parameters. Our main findings are the following: (i) ignoring baryonic effects leads to a greater than 5σ bias on the cosmological parameters Ω m and σ 8 ; (ii) restricting the analysis to the largest scales, that are mostly unaffected by baryons, makes the bias disappear, but results in a blow-up of the Ω m -σ 8 contour area by more than a factor of 10; (iii) ignoring baryonic effects on