In this Paper, we describe how we use stellar dynamics information to constrain the shape of the stellar initial mass function (IMF) in a sample of 27 early-type galaxies from the CALIFA survey. We obtain dynamical and stellar mass-to-light ratios, Υdyn and Υ*, over a homogenous aperture of 0.5 Re. We use the constraint Υdyn≥Υ* to test two IMF shapes within the framework of the extended MILES stellar population models. We rule out a single power-law IMF shape for 75 per cent of the galaxies in our sample. Conversely, we find that a double power-law IMF shape with a varying high-mass end slope is compatible (within 1σ) with 95 per cent of the galaxies. We also show that dynamical and stellar IMF mismatch factors give consistent results for the systematic variation of the IMF in these galaxies.