Taking advantage of the high acceptance and axial symmetry of the WASA-at-COSY detector, and the high polarization degree of the proton beam of COSY, the reaction p→p→ppη has been measured close to threshold to explore the analyzing power Ay. The angular distribution of Ay is determined with the precision improved by more than 1 order of magnitude with respect to previous results, allowing a first accurate comparison with theoretical predictions. The determined analyzing power is consistent with zero for an excess energy of Q=15 MeV, signaling s-wave production with no evidence for higher partial waves. At Q=72 MeV the data reveal strong interference of Ps and Pp partial waves and cancellation of (Pp)2 and Ss∗Sd contributions. These results rule out the presently available theoretical predictions for the production mechanism of the η meson.