In an Instagram revolt of the young, India’s “WhatsApp Uncles” are at a loss.

Prime Minister Narendra Modi, who for more than a decade has used social media to project an image of nearly divine infallibility, is facing perhaps his most formidable challenge in years in the form of a Gen Z-driven protest that has seized the digital narrative with videos, memes and authentic outrage.

As the demonstrators vent their anger at India’s economic failings and a lack of accountability, the signs and slogans in New Delhi at the main site of the protests — which spread this week to several other Indian cities — are aiming directly at Mr. Modi. Usually criticized only in whispers, the strongman leader has suddenly found himself the subject of jokes and taunts, with protesters defacing him on billboards and mocking him in verse, sharing the images online to an audience of millions.

The Indian state, its vast authority increasingly built around Mr. Modi’s image, has struggled to match the protesters’ creativity and tenacity. Anurag Minus Varma, the author of a book about how social media algorithms are transforming India, said the massive mobilization on the streets had broken a sense of fear and offered a release for pent-up anger.

“Because of the comfort of the crowd, now people can voice out their opinion,” Mr. Varma said. “And when they are voicing out their opinions, it is almost an outburst because every safety valve of democracy was closed by this particular regime.”