I assume that by NMDS you mean non-metric multidimensional scaling. As a starting point for NMDS, you need a distance matrix. Which distance measure to use is problem-specific but any distance measure can be used including Euclidean distance if it suits your problem. However, NMDS is often used when there are non-real valued items in the data, e.g. arbitrary ranking scores or categorical labels, for which Euclidean distance is not applicable. While metric MDS tries to preserve the pairwise distances between data points and requires this distance to be a metric, NMDS preserves the ranking of the distances and can be used with non-metric distances.
In short: Euclidean distance is suitable for NMDS but NMDS is often chosen for data to which Euclidean distance is not applicable.