Morgan, who has also been fined 40 per cent of his match fee after England took nearly four hours to bowl 50 overs in Bristol, will miss the fourth game of the Pakistan series at Trent Bridge tomorrow.
Every England player has also been fined 20 per cent of their match fees for maintaining the slow over-rate at Bristol.
Jos Buttler could take over the captaincy from Morgan at Trent Bridge after being rested at Bristol.
Another option is Yorkshire’s England Test captain Root, who has been an ever-present in the series. The final match is at Headingley on Sunday.
Richie Richardson, of the ICC’s elite panel of match referees, imposed the suspension on Morgan after England were ruled to be two overs short after time allowances were taken into consideration.
An ICC statement read: “In accordance with Article 2.22.1 of the ICC code of conduct for players and player support personnel, which relates to minor over-rate offences, players are fined 10 per cent of their match fees for every over their side fails to bowl in the allotted time, with the captain fined double that amount.”
Morgan’s ban is the result of him having also been found guilty of a minor over-rate offence during England’s ODI against the West Indies at Bridgetown in February.
The Bristol offence constituted his second minor over-rate offence within a 12-month period, so a one-match suspension was imposed.
Yorkshire’s England wicketkeeper-batsman Jonny Bairstow has also been reprimanded for breaching Level 1 of the ICC code of conduct.
Bairstow swiped the stumps with his bat after being bowled for 128 in the 29th over, as England successfully chased down a target of 359 to beat Pakistan.