"Sri Lanka Cricket ran out of funds after hosting the World Cup and sought government help to settle some payments," the minister told reporters in Colombo.
Sri Lanka, which lost the final to India by six wickets, hosted 12 matches during the World Cup, with others held in India and Bangladesh.
The island built brand new grounds in the southern town of Hambantota and the central town of Pallekele while nearly eight million dollars was spent to renovate the R. Premadasa stadium in Colombo.
"In total, we spent about five billion rupees ($46 million) to build the three World Cup venues," Aluthgamage said.
The minister said the governing body was forced to pledge the newly-built stadiums, along with income from upcoming tours, as collateral to raise funds to pay for the lavish tournament that ended on April 2.
The International Cricket Council (ICC), the sport's world governing body, has promised to pay about $25 million by way of hosting rights, the minister said.
Local media have been reporting that cash-strapped Cricket Sri Lanka has been unable to meet staff salaries, while suppliers, including hotels, were reluctant to host future teams due to a backlog in payments.
Sri Lanka are currently touring England and are lined up to face Australia, Pakistan and South Africa this year. The country is also due to host the World Twenty20 championships in 2012.
"It's not a crisis situation yet. We are confident the government will help us out," the minister said.
Since their World Cup final defeat, Sri Lanka's captain, vice-captain and selectors have quit while the head coach, Australian-born Trevor Bayliss, also ended his contract to take up his old job at New South Wales.
Sri Lanka won their sole World Cup in 1996 and emerged finalists in 2007.