Ultralight bosons such as axion-like particles are viable candidates for dark matter. They can form stable, macroscopic field configurations in the form of topological defects that could concentrate the dark matter density into many distinct, compact spatial regions that are small compared to the galaxy but much larger than the Earth. Here, we report the results of a search for transient signals from axion-like particle domain walls with the Global Network of Optical Magnetometers for Exotic physics searches (GNOME). We search the data, consisting of correlated measurements from optical atomic magnetometers located in laboratories all over the world, for patterns of signals propagating through the network consistent with domain walls. The analysis of data from a continuous month-long operation of the GNOME finds no statistically significant signals, thus placing experimental constraints on such dark matter scenarios.