The official start time, 9:08 am (local time), was about two hours after it was supposed to begin, according to NASA.
The glitch affected equipment known as the servicing and cooling umbilical (SCU), which supplies power and oxygen to the spacesuits worn by veteran US astronaut Peggy Whitson, 57, and her rookie counterpart, Jack Fischer, 43.
The problem involved "a small leak of water at the connection point of the service and cooling umbilical (SCU) as it was hooked up to Jack Fischer's spacesuit in the equipment lock section of the Quest airlock," said NASA commentator Rob Navias.
"This is not the suit itself. Fischer's suit itself is perfectly fine. The crew is perfectly fine," said Navias.
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"This is the connection point of the component in the airlock itself that provides power, oxygen, cooling water and communications lines to the two crew members while they are in the process of biding their time, pre-breathing pure oxygen, in the airlock itself."
According to NASA procedures, the spacewalk can go ahead with just one functioning SCU.
The plan is for the astronauts to take turns using the SCU, and alternate using battery power in their suits.
The astronauts will focus on one key task, to replace what is known as the ExPRESS Carrier Avionics, or ExPCA, box.
The box weighs 200 pounds (91 kilograms) on Earth, and routes data and commands to experiments inside the space station, Navias said.
"It has been exhibiting some thermal issues of late, so it is being replaced," explained Navias.
The spacewalk is the ninth of Whitson's career. She holds the record for most spacewalks by a woman.
NASA has experienced a series of problems with water leaking inside the astronauts' helmets, most notably in 2013 when water began filling Italian Luca Parmitano's headpiece, forcing him to cut short his spacewalk and make an emergency re-entry into the space lab.
NASA's bulky white spacesuits are aging, and the same models have been in use for four decades.