This can be done via
gsettings set org.gnome.nautilus.icon-view text-ellipsis-limit "['1']"
The key's description:
A string specifying how parts of overlong file names should be
replaced by ellipses, depending on the zoom level. Each of the list
entries is of the form "Zoom Level:Integer". For each specified zoom
level, if the given integer is larger than 0, the file name will not
exceed the given number of lines. If the integer is 0 or smaller, no
limit is imposed on the specified zoom level. A default entry of the
form "Integer" without any specified zoom level is also allowed. It
defines the maximum number of lines for all other zoom levels.
Examples: 0 - always display overlong file names; 3 - shorten file
names if they exceed three lines; smallest:5,smaller:4,0 - shorten
file names if they exceed five lines for zoom level "smallest".
Shorten file names if they exceed four lines for zoom level "smaller".
Do not shorten file names for other zoom levels. Available zoom
levels: smallest (33%), smaller (50%), small (66%), standard (100%),
large (150%), larger (200%), largest (400%)
If you want to do this for the desktop as well, from Can we (easily) turn off the line wrapping of icons on the desktop?:
gsettings set org.gnome.nautilus.desktop text-ellipsis-limit 1