Aims. T Pyx is the first recurrent nova ever historically studied. It was seen in outburst six times between 1890 and 1966 and then not for 45 years. We report on near-IR interferometric observations of the recent outburst of 2011. Methods. We obtained near-IR observations of T Pyx at dates ranging from t = 2.37 d to t = 48.2 d after the outburst, with the CLASSIC recombiner located at the CHARA array and with the PIONIER and AMBER recombiners located at the VLTI array. These data are supplemented with near-IR photometry and spectra obtained at Mount Abu, India. We compare expansion of the H and K band continua and the Brγ emission line, and infer information on the kinematics and morphology of the early ejecta. Results. Slow expansion velocities were measured (≤300 km s −1 ) before t = 20 d. From t = 28 d on, the AMBER and PIONIER continuum visibilities (K and H band, respectively) are best simulated with a two-component model consisting of an unresolved source plus an extended source whose expansion velocity onto the sky plane is lower than ∼700 km s −1 . The expansion of the Brγ lineforming region, as inferred at t = 28 d and t = 35 d, is slightly larger, implying velocities in the range 500−800 km s −1 , which is still strikingly lower than the velocities of 1300−1600 km s −1 inferred from the Doppler width of the line. Moreover, a remarkable pattern was observed in the Brγ differential phases. A semi-quantitative model using a bipolar flow with a contrast of 2 between the pole and equator velocities, an inclination of i = 15• , and a position angle PA = 110• provides a good match to the AMBER observables. At t = 48 d, a PIONIER dataset confirms the two-component nature of the H band emission, consisting of an unresolved stellar source and an extended region whose appearance is circular and symmetric within error bars. Conclusions. These observations are most simply interpreted within the frame of a bipolar model, oriented nearly face-on. This finding has profound implications for interpreting past, current, and future observations of the expanding nebula.