Arjuna, who led Sri Lanka to its only World Cup victory in 1996, sought the position of vice president but lost by 22 votes to businessman Jayantha Dharmadasa, according to official results.
His brother Nishantha Ranatunga stood for president of crisis-ridden Sri Lanka Cricket but lost by 32 votes to businessman and politician Thilanga Sumathipala.
There was no immediate comment from the Ranatunga brothers, both of whom had previously held top positions at Sri Lanka Cricket.
Sri Lanka’s then-sports minister Navin Dissanayake had sacked the previous board last April amid allegations of rampant corruption and appointed an interim committee pending fresh elections.
However, his move was criticised by the sport’s world governing body the International Cricket Council, which had insisted that Sri Lanka Cricket hold elections. Cricket clubs affiliated to the island’s governing body were eligible to vote Sunday and to elect new office-holders.