While the number of riders caught up in the malfunction is not yet known, some have shared their stories with local media.
Phoning the Orlando Sentinel, Chris Edenfield and his disabled mother were trapped for hours.
"We've cracked open the emergency kit a while ago for water; it's just a nightmare right now,"
Disney World said that no injuries were reported and it was working with each guest "regarding impacts to their visit".
Skyliner is just under a week old, and was opened to much public excitement. Ahead of the breakdown social media was abuzz with positive feedback and multiple exclamation marks.
"Seriously soooooooo obsessed guys," wrote one fan account @disneywithlocals.
The new cable car system and its 300 colourful gondolas should allow visitors to traverse the whole park in 11 minutes.
Described as a "grand, state-of-the-art gondola system", it connects the Hollywood Studios and Epcot Park to Disney hotels.
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"We have a team diligently looking into the cause of Saturday's malfunction on the Epcot line of the Disney Skyliner," Disney World said in a statement to USA Today.
"We have been in contact with the guests, many of whom were on the Skyliner for more than three hours until we were able to restart the system. We express our sincere apologies for the inconvenience and continue to work with each guest individually."
New theme park attractions have historically suffered from teething problems.
In 1955 the opening of the company's first Disney Land theme park was legendarily problematic.
The public opening on July the 17th became known in Disney staff folklore as "Black Sunday".
As well as the park being awash with counterfeit tickets and wet paint and unfinished attractions, at six attractions broke down, the Mark Twain riverboat sank and live tigers escaped from their cages.
The Skyliner's breakdown in comparison was relatively minor, if embarrassing for Disney and extremely uncomfortable for any passengers caught up in it.