We present the first lattice QCD calculation of electromagnetic form factors of a tetraquark, focusing on the $T_{bb} = bb\bar u \bar d$ with quantum numbers $I(J^P) = 0(1^+)$. The electromagnetic current probes the charge monopole, magnetic dipole and the electric quadrupole distributions within the tetraquark. From it, we find evidence that its structure consists of a compact heavy diquark $[bb]$ in spin one, color-antitriplet configuration, and a light antidiquark $[\bar u \bar d]$ in spin zero, color-triplet configuration. The computations were performed on a single CLS ensemble with $N_f = 2+1$ dynamical quarks at a lattice spacing $a\approx 0.064$ fm and with a pion mass $m_\pi \approx 290$ MeV.