The Asian team put in a spirited display against the tournament hosts and defending champions Australia in their final game of the tournament in Adelaide on Friday but went down by four runs.
Afghanistan finished their campaign with three defeats from their five matches while they were unlucky that two of their games were rained out.
The 37-year-old Nabi, in a statement posted on his Twitter account, said he was resigning as the team's leader, citing disagreements with the selectors and management.
He wrote: "Our T20 World Cup journey came to an end, with a result that not us nor our supporters were expecting. We are as frustrated as you are with the outcome of matches.
"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.
"Moreover, in some of the last tours the team management, selection committee and I were not on the same page which had implications on the team balance.
"Therefore, with due respect, effectively immediately I announce to STEP DOWN as a CAPTAIN & will continue to play for my country when the management & team need me.
"I thank every single one of you from the bottom of my heart who came to the grounds despite matches being affected by the rain and those who supporters us worldwide, your love truly means a lot to us. Long live Afghanistan."
Nabi took over as Afghanistan skipper before the 2021 T20 World Cup in the UAE after Rashid Khan's resignation from the role.
One of the stars of the side, Rashid announced he had quit as captain less than half an hour after the selectors had named their squad for that 2021 event, saying he had not been consulted.