Wolff said he was speaking out because some of the abuse directed at the Formula One team could impact on engineers and other employees.
"I don't want to even ignore this bunch of lunatics who think that we would harm a driver who is our driver, who has been a double world champion for us," the Austrian told reporters.
"He (Hamilton) hasn't let us down, and we wouldn't let him down. This is a mechanical sport and these things happen."
Despite the Briton's success with Mercedes, there have always been some who believe the German manufacturer really wants a German champion.
Hamilton has not won a race since he took his third title in Texas in October and has suffered mechanical problems in his last two races, starting from the back of the grid in China and 10th in Sochi.
He is now 43 points behind Rosberg after four races.
Wolff suggested some of the critics were "lying in their beds with their laptops on their chests" and were not to be taken seriously.
"The reason why I am being vocal about it is that I want to protect the guys," he said.
"They are being hit by comments that are just inexcusable and unfair and abusive without reason. If some of the guys read those comments they might take it personally."
Hamilton would have had to start from the pit lane in Russia on Sunday had Mercedes not, as Wolff pointed out, "moved heaven and earth" to fly essential parts from Britain overnight.
Wolff said non-executive chairman Niki Lauda organised the private jet while Formula One's commercial supremo Bernie Ecclestone "sorted" the Russian customs.
Hamilton, who has 3.3 million followers on Twitter and is active on various social media platforms, understood the hurt felt by fans but assured them the team was making every effort.
"The people...are feeling the same pain I'm feeling," he said. "They're feeling the hurt and emotions you go through because we're connected in that way and its a beautiful thing.
"In any sport or any situation the easiest thing is to jump to the negative and I just want to assure them that my guys are doing a fantastic job and it's not their fault."
(Editing by Ed Osmond)
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