Morgan, who was deputising as skipper with Stuart Broad rested, has suffered a hand injury and England will now turn to Kent spinner Tredwell as a third option.
A post on the England and Wales Cricket Board's official Twitter feed read: "#Eoin16 ruled out of NatWest IT20 vs #BLACKCAPS tonight with right hand injury. James Tredwell will captain the side."
Kevin Pietersen is set to make his long-awaited England return in the match.
Pietersen has not pulled on an England shirt since he was forced home from the reverse tour of New Zealand in March with a knee injury.
A prolonged recovery had threatened his Ashes place but, after marking his return to competitive action with an unbeaten 177 for Surrey at the weekend, Pietersen is ready to resume his England duties on his 33rd birthday today.
The right-hander warmed up for tonight's game with a specifically-organised training session at the Oval nets yesterday.
Overseen by spin bowling coach Mushtaq Ahmed and with none of his team-mates present, Pietersen was put through his paces for 20 minutes by a pool of net bowlers.
He showed no obvious sign of discomfort and at one point launched one of the bowlers out of the stadium.
Immediately after returning to the dressing-room Pietersen posted a picture of himself in his England training kit on Twitter, which read: "Back with ENG!"
Tonight's game will be Pietersen's only opportunity to impress in an England shirt against international opposition before the Ashes begin at Trent Bridge on July 10. He has also been included for England's Ashes warm-up match against Essex which starts on Sunday.
England have not lost any of their past eight bi-lateral series in the shortest format but are in danger of ending that run after narrowly failing to chase down 201 for four.
A weakened England, without any of their Test stars, appeared on course to secure their highest ever Twenty20 chase thanks mainly to Luke Wright's quickfire 52. But late wickets slowed them before Ravi Bopara failed to hit the final ball for six, which would have sent the game into a super over.
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