The study of fungal cells is of great interest due to their importance as pathogens and as fermenting fungi and for their appropriateness as model organisms. The differential pressure between the hyphal cytoplasm and the bordering medium is essential for the growth process, because the pressure is correlated with the growth rate. Notably, during the invasion of tissues, the external pressure at the tip of the hypha may be different from the pressure in the surrounding medium. We report the use of a method, based on the micropipette-aspiration technique, to study the influence of this external pressure at the hyphal tip. Moreover, this technique makes it possible to study hyphal growth mechanics in the case of very thin hyphae, not accessible to turgor pressure probes. We found a correlation between the local pressure at the tip and the growth rate for the species Arpergillus nidulans. Importantly, the proposed method allows one to measure the pressure at the tip required to arrest the hyphal growth. Determining that pressure could be useful to develop new medical treatments for fungal infections. Finally, we provide a mechanical model for these experiments, taking into account the cytoplasm flow and the wall deformation.