The awards - known as the 'Oscars of sport' - took place in the Brazilian city last March and a contract had been agreed for this year's event but that has now been cancelled.
It comes after the cancellation of the Soccerex conference last month, and amid ongoing delays in the preparation for the football World Cup.
The Laureus foundation said in a statement: "Laureus and the state of Rio de Janeiro have agreed that the 2014 Laureus World Sports Awards will not be staged in Rio. Laureus will announce its plans for this year's awards shortly."
FIFA presdient Sepp Blatter has said Brazil is the least-prepared of any World Cup host he has known, while the International Olympic Committee has also expressed concerns that Rio 2016 organisers have no time to lose.