Nabi, 37, will continue as a player but said he and the selectors were not “on the same page”.
“From the last one year, our team preparation was not to a level that a captain would want it or needed for a big tournament,” he said in a statement on Twitter.
“Moreover, in some of the last tours, the team manager, selection committee and I were not on the same page which had implications on the team balance.
“Therefore, with due respect, effective immediately, I announce to step down as a captain and will continue to play for my country when the management and team need me.”
Afghanistan, coached by former England batsman Jonathan Trott, finished the Super 12 stage in Australia without a win.
They had two washouts and two losses to sit bottom of the six-team table in Group 1.
Nabi, a middle-order batsman and off-spinner, has played 104 T20 matches for Afghanistan since his debut in 2010.
Afghanistan’s latest defeat came after they fell four runs short in their chase of 168 despite an unbeaten 48 by Rashid Khan, who came to bat at number eight.
“It showed the skill and talent of the players that we have got, but also the situation awareness that we lack in parts and we saw that against Sri Lanka, we have seen it again tonight,” Trott told reporters before Nabi’s announcement.
On being asked on Rashid’s promotion up the order, Trott said, “I think the other batsmen in the side start taking more responsibility for their innings and with the responsiblity that they are charged with.
“There are times when the players need to stand up and accept the pressure that comes with playing international cricket and you need to perform better.”
The team has come on leaps and bounds with players initially learning the game in refugee camps in Pakistan after fleeing the 1979-1989 Soviet occupation.
“I look at it and I realised how fortunate and privileged I was growing up in a country where sport is so well catered for and encouraged and is a way of life really,” said Trott, who took up the Afghanistan job in July.
“So to see these guys and hear their stories about their background of growing up and the things that they have had to overcome, areas they have come from and get to be here in Adelaide playing under the bright lights in front of over 18,000 people and a worldwide audience…
“They could be better with regards to structure but as far as players, I don’t have an issue with any of them.”
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