Photoassociation of ultracold lithium atoms into bound vibrational levels of the AΣu+1 excited state is used to probe the XΣg+1 ground-state interaction potential of Li26 and Li27. It had been predicted that the s-wave photoassociation signal strength would pass through a minimum as a function of vibrational level for positive s-wave scattering length. We report the observation of this novel effect, and use the location of the minimum to precisely determine the singlet s-wave scattering length for both isotopes. The sensitivity of this technique is demonstrated by distinguishing the minima for collisions involving Li7 atoms in different hyperfine states.