Yes, you can install Postman using these commands:
wget https://dl.pstmn.io/download/latest/linux64 -O postman.tar.gz
sudo tar -xzf postman.tar.gz -C /opt
rm postman.tar.gz
sudo ln -s /opt/Postman/Postman /usr/bin/postman
You can also get Postman to show up in the Unity Launcher:
cat > ~/.local/share/applications/postman.desktop <<EOL
[Desktop Entry]
Encoding=UTF-8
Name=Postman
Exec=postman
Icon=/opt/Postman/app/resources/app/assets/icon.png
Terminal=false
Type=Application
Categories=Development;
EOL
You don’t need node.js or any other dependencies with a standard Ubuntu dev install.
See more at our blog post at https://blog.bluematador.com/posts/postman-how-to-install-on-ubuntu-1604/.
EDIT: Changed icon.png location. Latest versions of Postman changed their directory structure slightly.