4 December 2014 10:52 am
The ban was triggered because it was Cook's second slow over rate offence within 12 months.
England were ruled to be one over short of its target at the end of the rain-reduced game in Hambantota.
Cook was also fined 20% of his match fee and the rest of the team docked 10% by the International Cricket Council.
England coach Peter Moores told BBC Test Match Special: "We knew Cook was on the verge of a ban, the bonus is that it wipes the slate clean before the World Cup."
Eoin Morgan will captain England in Cook's absence in the fourth ODI of the series in Colombo on Sunday.
England trail the seven-match series 2-1.(BBC)