Short-period α-Sn/Ge strained-layer superlattices have been prepared on [001] Ge substrates by low-temperature molecular-beam epitaxy. We have achieved almost-defect-free and thermally stable single-crystalline structures. Photocurrent measurements in a series of Sn1Gem (m>10) superlattices reveal a shift of the fundamental energy gap to smaller energies with decreasing Ge layer thickness m, in good agreement with band-structure calculations. A direct fundamental energy gap is predicted for a slightly increased lateral lattice constant in α-Sn/Ge superlattices.