BEIJING—A forceful campaign of intimidation against China's most influential Internet users has cast a chill over public debate in the country and called into question the long-term viability of its most vibrant social-media platform.

In an offensive that some critics have likened to the political purges of the Mao era, Beijing has recently detained or interrogated several high-profile social-media figures, issued warnings to others to watch what they say and expanded criminal laws to make it easier to prosecute people for...