Citizens Advice Scotland wants Glasgow 2014 to introduce the prohibition in line with that placed on adverts for alcohol and tobacco products at major sporting occasions.
It made the call after it discovered it was supporting more than 100 people a week who found themselves in crippling debt after taking out expensive loans. The resulting financial problems they faced often destroyed their health and relationships, the service said.
Interest rates on payday loans often exceed 5000% and people who originally borrow a couple of hundred pounds can quickly find themselves owing thousands as they struggle to pay off the debt.
Their popularity has soared in recent years and many people with financial difficulties have turned to payday lenders to find money for food and fuel.
Susan McPhee, head of policy at Citizens Advice Scotland, said the damaging impact of the loans should be regarded in a similar way to tobacco and alcohol.
She said: "Twenty years ago it was the norm for tobacco and alcohol companies to sponsor big sporting occasions. Today it is generally accepted this is inappropriate and products which have a damaging impact on people should be excluded from sponsoring such high-profile events.
"We believe payday loans should be seen in this same category and banned from this year's Games.
"Over the last few years we have published considerable evidence about the damage done by payday loan companies to our clients.
"Common problems include misleading adverts, massive interest rates, failure to assess applicants' financial backgrounds, aggressive efforts to reclaim debts and trapping people in further debt through 'roll-over' loans.
"We don't believe companies who operate like this have any place in a great sporting occasion.
"All Scots will remember how proud we were when Glasgow was awarded the Games, and we're all looking forward to a brilliant summer hosting this gala of sporting excellence in our great city. That pride will be tainted if we see the city plastered in banner adverts for companies which trade in trapping families in misery and debt."
The service has written to the Games's organisers calling for the ban. In its response the Games team confirmed no such sponsorship deals were in place, but said they were unable to take a position on the issue.
Ms McPhee added: "I'm sorry the organisers feel they are unable to take a position on this issue, but having opened the dialogue we will continue to engage with them and to press our case. There are plenty of other good companies out there whose money would be just as good, without advertising damaging products. The Glasgow Games has a unique opportunity here to set an example."
A Glasgow 2014 spokesman said: "Glasgow 2014 has no sponsorship partners of this type at present and no plans to develop them."
Last year, Scottish Enterprise Minister Fergus Ewing called for a cap on interest rates charged by payday loan companies to be brought forward by the UK Government from January 2015 to next April. He said: "The uncontrolled growth of the payday loan industry has been the cause of one of the most extreme social hardships of modern times, a cause of great social misery."
A number of Scottish local authorities, including Glasgow, do not allow payday loan companies to rent their properties.