The group says it "wants to provide a substantial incentive for anyone who knows the truth to come forward."
The Boeing 777 disappeared on March 8 while carrying 239 people from Malaysia to Beijing.
Calculations made from transmissions the plane sent to a satellite show the flight ended in a patch of the southern Indian Ocean. But searchers have found nothing there, leading to speculation and conspiracy theories over the fate of the plane and its passengers.
Many family members of those on board have been highly critical of the search. Some have stated they believe it likely that the plane has landed somewhere, meaning their loved ones might be alive.
The group of relatives started its fundraising campaign on the crowd sourcing website Indiegogo.
Just under 24 hours after it launched, the campaign had raised just over $5,000.
In a posting on the site, it said the money would be first used as a reward for information. It said it also planned to engage a licensed private investigation company to follow up on that information.
"Someone somewhere knows the truth, they could be your neighbor, work colleague, brother, sister, mother or father," Peter Weeks, whose brother was on the plane, said on the Indiegogo page.
The international search for the plane, unprecedented in aviation history, is on hold for two months while the seafloor is mapped and specialized equipment to work in the deep water is brought in. The focus of the hunt is a 700 kilometer by 80 kilometer (430 mile by 50 mile) swath of ocean where searchers believe the plane crashed.
Experts say it is quite possible it will never be found.