"The name Muralitharan should be expunged from cricket records," Rowan was quoted as saying in Queensland's Toowoomba Chronicle.
Muralitharan, 30, the third leading wicket-taker in Tests and one-day internationals, was no-balled for throwing on the 1995-96 and 1998-99 tours of Australia. His action was subsequently cleared by the International Cricket Council.
He was taunted by Australian crowds in triangular one-day series matches earlier this month and has said he may not tour the country again because of the crowd's behaviour.
Rowan said relations were strained between Sri Lanka and the England and Australian camps because of resentment over Muralitharan's action.
"No player will make a comment because they will be accused of racism and the various boards and the ICC will do nothing for the simple reason of the certainty of racist allegations," Rowan said.
"The actions of cricket authorities in permitting and encouraging this man to continue in cricket are incomprehensible and a travesty of justice."
Rowan was the umpire at the other end when Colin Egar no-balled Australia fast bowler Ian Meckiff for throwing in his only over in the first Test against South Africa in December, 1963. Meckiff subsequently retired from all cricket.
