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Primordial magnetic fields (PMFs) create a large squeezed-typenon-Gaussianity in tensor perturbation, which generates non-Gaussiantemperature fluctuations in the cosmic microwave background (CMB). We for thefirst time derive an observational constraint on such a tensor non-Gaussianityfrom observed CMB maps. Analyzing temperature maps of the WMAP 7-year data, wefind that such a tensor non-Gaussianity is consistent with zero. This gives anupper bound on PMF strength smoothed on $1 ~ {\rm Mpc}$ as $B_{1 ~ \rm Mpc} <3.1 ~{\rm nG}$ at $95%$ C.L.

First observational constraints on tensor non-Gaussianity sourced by primordial magnetic fields from cosmic microwave background