A three-member bench of the Supreme Court asked the sports ministry to hold elections and make the appointments by July 6, a court official said.
The sports minister had been using his powers till now to appoint officials to the interim committee.
The court order came after the local United Southern Sports Club filed a fundamental rights petition on behalf of clubs who have not been able to elect officials to the board.
A lack of elected office bearers has often been blamed for problems plaguing the sport in the country.
Australia's Trevor Bayliss, who recently quit as Sri Lanka coach after a four-year stint with the team, had underlined the need for a strong and stable cricket administration.
"Good teams like Australia usually have got strong or good management backing the team up. That's an area we can improve here," he said in his parting comments.