The drawing, entitled 'Ceasefire: boredom sets in in Donetsk', depicts the inhabitants of separatist-controlled eastern Ukraine standing amid ruins and rubble wondering, 'How about we do something with some cartoonists?'
"It is an abomination, not freedom of expression," Pushkov, who is known for his controversial statements, wrote on his Twitter account.
Russia initially welcomed an historic march against terrorism in Paris after January's deadly attacks on the weekly, but many media and Russian officials have subsequently turned against Charlie Hebdo, saying it disrespects religious followers.
Hundreds of thousands of protesters also gathered on January 19 in Grozny, capital of the Chechnya region, to denounce the cartoons of the satirical newspaper.