Critics say Tanzania is too poor to pay for the system
The decision threatens to re-open a cabinet row over the sale of the £28m BAE Systems device, which was approved with the award of an export licence last December.
Ms Short said Tanzania, one of the world's poorest countries, could have opted for an adequate alternative which cost a quarter of the price.
The Department for International Development (DfID) has confirmed the aid has been delayed until a report into whether the African state has breached its commitments to alleviate poverty is completed.
Moral duty
The decision to allow BAE Systems to sell Tanzania the equipment prompted a cabinet row, with Ms Short and Chancellor Gordon Brown opposing the sale.
They said supporters of the deal - including Tony Blair, Trade and Industry Secretary Patricia Hewitt and Defence Secretary Geoff Hoon - were wrong because Tanzania was receiving international money to tackle food shortages.
After the deal went through Ms Short told the BBC the government had a moral duty to put concern for the world's poor above commercial interests.
The Tanzanian President, Benjamin Mkapa, has said his country needs it to ensure air safety.
'No rift'
Ms Short denied the decision to hold back the aid was aimed at reopening the rift with her colleagues.
She said: "There is no cabinet rift. The export licence has been granted.
"The decision to delay the release of budgetary support pending a review of Tanzania's air traffic control system was based on Tanzania's commitment to poverty reduction."
DfID officials said the department was awaiting the outcome of an inquiry by the International Civil Aviation Organisation (ICAO) into whether the purchase breached Tanzania's poverty reduction strategy.
The ICAO's report was expected to be published next week.
One official said: "If it is found that Tanzania is not sticking to its poverty reduction strategy, then there will be an issue in releasing that budgetary support."