We have characterized Czochralski‐grown undoped AlSb single crystals by low‐temperature photoluminescence and photoluminescence excitation spectroscopy. An excitonic band‐gap energyEgx=1.667±0.001 eV of AlSb was determined. In all samples we detect a dominant donor and acceptor. The donor binding energyED=151±3 meV and acceptor binding energyEA=37±3 meV are deduced from donor‐acceptor pair luminescence and the excited states of the acceptor from selective pair excitation. We tentatively identify the donor as sulfur and the acceptor as carbon.