The letter, signed by Russian Space Systems deputy head Ivan Golub, proposed that Popovkin leave his post, accusing him of making confusing orders and of "legal nihilism."
Upon Popovkin's appointment to his post, "There began events that are impossible to understand or accept," the letter said, Gazeta.ru reported. "Your legal nihilism shows that a high-ranking leader can allow himself everything, with impunity, that once seemed unthinkable to us."
Popovkin "created an uncontrolled...group of individuals that have received limitless authority," the letter said. "You can continue to surprise us, but maybe you leave quietly. We're ashamed."
The Russian version of the Russian Space System website, where the letter was reportedly posted, was offline Wednesday afternoon.
The letter appeared to be a response to comments made by Popovkin on Monday, the day he returned to work after being in the hospital for more than a week under mysterious circumstances. Media reports speculated that he was receiving treatment for head injuries after taking part in a fistfight.
He linked the reports to the heads of space industry contractors, who he said felt threatened by reforms he has initiated.
The news reports speculating about the reasons for Popovkin's hospitalization "gave me to understand that certain heads of Roscosmos enterprises have something to lose as a result of reforms undertaken in the industry," Popovkin said, RIA-Novosti reported.
"Order in the industry will be established, and financial flows will become transparent and open," he said, alluding to alleged corruption schemes by space industry contractors.
Popovkin was hospitalized on March 7, for what he said was emotional and physical stress due to a heavy workload.