Using data samples collected at center-of-mass energies of s√=4.009, 4.226, 4.257, 4.358, 4.416, and 4.599 GeV with the BESIII detector operating at the BEPCII storage ring, we search for the isospin violating decay Y(4260)→J/ψηπ0. No signal is observed, and upper limits on the cross section σ(e+e−→J/ψηπ0) at the 90% confidence level are determined to be 3.6, 1.7, 2.4, 1.4, 0.9, and 1.9 pb, respectively.