Nick Forbes, leader of Newcastle City Council, said the deal represented a "profit at any price culture" at the club and warned of the possible social consequences.
Nick Forbes: "I'm appalled and sickened that they would sign a deal with a legal loan shark.
"We see the devastating consequences of people getting into financial difficulty and we spend a lot of money each year helping people who are in debt through companies like this.
"It's a sad indictment of the profit at any price culture at Newcastle United.
"We are fighting hard to tackle legal and illegal loan sharking and having a company like this right across the city on every football shirt that's sold undermines all our work.
"I fear the long-term social consequences of the decision and I will be writing to Mike Ashley and asking for him to fund the extra debt advice that we will need to provide as a result.
"Newcastle United is a role model for thousands of people so what they do matters.
"It sets the tone for the city and I don't want this to be a city built on an image of cheap and irresponsible debt."
Ian Lavery, MP for Wansbeck: "A city like Newcastle and the region should not have any ties with an organisation like Wonga.
"This business makes profits off the back of deprived people who are desperate and who are the most vulnerable in society.
"It's an absolute outrage and I now won't set foot into the stadium."