Uber and other companies in the sharing economy have had to spend millions fighting city and state regulators that try to stifle innovative services. Now New York has moved to crush the home-sharing service Airbnb in the city’s five boroughs.

Governor Andrew Cuomo late Friday signed legislation that would impose a fine of up to $7,500 on anyone who advertises a short-term rental apartment on a home-sharing site. That’s more than the penalty for drunk driving.

This...