Hughes had his wrecked car into a work of art
The charges stem from a crash in which Hughes, the art critic for Time magazine, was almost killed in May 1999 while in Australia filming a documentary for the BBC.
He spent five weeks in a coma after his rented car collided with another vehicle, near Broome, in Western Australia.
Three occupants of the other car were also hurt, one seriously.
The warrant, which is only effective in the state, was issued by Perth Magistrates' Court.
The court set another hearing date, 4 July, to allow Hughes time to return.
Hughes issued a statement in New York, where he lives, explaining his non-appearance, Australia's ABC radio reported.
He was quoted as saying his injuries from the crash were still serious, and had prevented him from making the long journey to Australia.
He suffered multiple factures and numerous other injuries in the crash.
The two dangerous driving charges were brought against him in May 2000, but were dismissed after prosecutors failed to call two key witnesses who had been charged with conspiracy to pervert the course of justice.
In September 2000, Australia's Supreme Court ordered a new trial on the same charges after an appeal by Western Australia's director of public prosecutions.
In January, Hughes's wrecked car went on show in an art gallery in Perth.
The installation, by artist Danius Kesminas, consisted of the car, crushed into a cube displayed inside a clear plastic box.