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Off-spinner James Tredwell will lead the side in the former Ireland batsman's absence after Morgan was ruled out with a right hand injury.
The ECB said the injury to Morgan, leading the team in the place of the rested Stuart Broad, was expected to be "short-term".
Tredwell will be the latest Kent player to lead his national team, after a wait of nearly 25 years since Chris Cowdrey captained the Test team against the West Indies in July 1988.
"It is a great honour that I will lead out the team this evening," Tredwell said Thursday.
"Firstly to have had the opportunity to play for England, now to captain the team is something you dream of."
New Zealand won the first of the two-match series by five runs at The Oval on Tuesday.
"Hopefully as a group we can go one better than Tuesday."
Morgan's absence helped England avoid a difficult decision over to whom to drop in order to free up a space for returning batsman Kevin Pietersen.
South Africa-born shotmaker Pietersen has been out of England action since March with a knee injury and was sidelined from all cricket until making a superb unbeaten 177 for Surrey in a County Championship match last weekend.
