The victim, a photographer's assistant, was shot in the chest and stomach with a pump-action shotgun and was in a critical condition, police and the newspaper said.
The shooter fled the scene and was still at large several hours after the attack, which occurred around 10:15am (1445 IST).
Just over an hour later, witnesses described shots being fired -- also from a pump-action shotgun -- outside the headquarters of Societe Generale bank in the La Defense business district.
Police helicopters were circulating over the French capital's most famous avenue, apparently looking for the gunman.
Police could not immediately confirm a link between all of today's reported incidents but said that CCTV images of the shooter suggested he was the same man who had stormed into the Paris headquarters of news channel BFMTV on Friday.
In that incident, the gunman emptied several cartridges from his shotgun before warning a senior editor: "Next time, I will not miss you."
"I saw this guy with a cap and a shotgun, a pump-action shotgun, in his hand," Alvarez told AFP. "I don't think he was necessarily targeting anyone, he shot in the air then into a window. The first shot shocked everyone into silence and then the second caused a general panic. Then he ran away down the steps to the street."
As news of the Liberation shooting broke, Police were quickly deployed at major media offices in Paris for fear of further attacks.
Liberation executive Nicolas Demorand said the shooting in the paper's entrance hall had left staff traumatised.
"If papers and other media have to become bunkers, something has gone wrong in our society."
A police security cordon had been erected around Liberation's editorial offices in central Paris.
The newspaper said the injured man worked as an assistant to one of the photographers for its Next supplement.
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