Global warming has an increasing impact on the availability of water for agriculture. Crops tolerant to high temperatures and drought, such as cowpea (Vigna unguiculata L. Walp.), have an added value in the near future. The main objective of this study was to evaluate the effect of drought on seed germination and seedling emergence of cowpea genotypes, in order to screen the most tolerant genotypes. Seeds from 58 cowpea genotypes all over the world were submitted to two stress conditions, induced by PEG-6000 (corresponding to osmotic potentials of −0.75 bars and −1.5 bars). Germination and seedling growth parameters, vigor index and proline content were determined to assess drought tolerance. The results revealed significant differences of all parameters among genotypes after treatments and interaction of both. Water stress caused a general decrease in germination and seedling growth, while an increase in proline content was observed. A high variation of drought responses were detected among genotypes, being possible to select seven genotypes (C11, C18, C44, C46, C47, C50 and C54) as tolerant to drought at germination stage. These results will be useful to select the best suitable parents for insertion in future breeding programs.