Discovery is due to lift off from Cape Canaveral in Florida on Tuesday afternoon, after two weather-related delays during the weekend.
"We are going tomorrow," Lisa Malone told reporters at the Kennedy Space Centre.
Nasa announced the discovery of the crack one day before shuttle's planned liftoff with seven astronauts on a crucial mission for US space ambitions.
Inspectors found the crack overnight after the tank was emptied of its liquid hydrogen and liquid oxygen fuel, following the second straight launch delay on Sunday.
The orange-hued fuel tank's foam insulation has perplexed Nasa ever since the 2003 Columbia disaster, which was caused by loose foam that pierced the shuttle's heat shield during liftoff and doomed its return to Earth.
The US space agency spent more than a billion dollars to fix the problem, only to see a piece of foam fall off Discovery's fuel tank in the first post-tragedy launch in July 2005. The debris missed the shuttle, however.
Prior to the current planned launch, Michael Griffin, Nasa administrator, expressed confidence that no large chunks of foam would shed from Discovery's second mission since Columbia.
The crack was about one-eighth to one-quarter of an inch deep and five inches (12.5 centimetres) long, Nasa spokesman George Diller said. It was found in the insulating foam on a bracket that holds an oxygen feed line.
The discovery came after storms scuttled two weekend launch attempts, forcing Nasa to take a break on Monday to rest the launch crew and recharge fuel cells that power the shuttle in orbit.
Diller said the crack might have been caused by the unloading and reloading of fuel during the past two days into the huge external tank - about the height of the Statue of Liberty - that helps power Discovery into orbit.
Discovery's five men and two women astronauts are due to fly to the International Space Station (ISS) on a mission aimed at improving shuttle safety.
During the 12-day flight, the astronauts will test new procedures to boost safety as well as deliver critical equipment and supplies to the ISS.
They will drop off European Space Agency astronaut Thomas Reiter of Germany, who will join the ISS's two other crew members for a long-term stay, and will perform two space walks.
The mission comes three years after the shuttle Columbia disintegrated while returning to Earth.
Nasa grounded its 25-year-old fleet last year after debris fell off Discovery's fuel tank.