We succeeded in observing the two-photon absorption of germanium for both the direct and the indirect gaps, using the Vanderbilt free-electron laser. The two-photon absorption for the indirect gap was found to be 3 orders of magnitude smaller than the direct gap. The indirect-gap threshold position indicates that the two-photon absorption is assisted by an LO phonon, providing a long-delayed positive test of the Bassani-Hassan predictions.