The petition first posted on the website Change.org on Thursday came after the premier advised a low-paid lecturer to go into business if he wanted to make money.
Medvedev’s comments — seen as out-of-touch and uncaring — unleashed a torrent of criticism in the press and on social media.
“The cabinet should be led by a person who is competent, educated and cares about the country,” wrote the petition’s author, Alexander Li.
“We are seeing the opposite right now.”
The Duma, the lower house of Russia’s parliament, is obliged to debate any petition that gets 100,000 signatures.
At a youth education forum on Tuesday, Medvedev was asked by a university lecturer from the impoverished Dagestan region why teachers receive only around 15,000 rubles ($230) per month, while police are significantly better paid.
“There’s no need to compare,” Medvedev said. “The issue is what you choose in life.”
Teaching, he said, “is a vocation. If you want to make money, there are a bunch of great places where you can do that quicker and better in business. And you didn’t go into business.”
Medvedev — who served as president from 2008 to 2012 between Putin’s presidential terms — added that a “modern energetic teacher” should be able to find ways to “earn something extra.”
Medvedev, who lectured at the law faculty of Saint Petersburg State University in the 1990s, also cited himself as an example of a teacher who succeeded in making a living.
“I just gave a lot of lectures, held seminars,” he said. “Overall I was able to make ends meet.”
Official statistics show the average monthly salary in Russia is around 37,000 rubles (507 euros, $566). Teachers make an average 32,000 rubles per month but the figure varies greatly depending on the region.
In Dagestan, teachers earn a monthly average of 18,000 rubles, Kommersant daily reported.