But Fleming said he wants to continue playing in the side and stay in charge of the Test team.
The 34-year-old opening batsman had been in charge for 10 years, leading his country in 218 one-day internationals, including three World Cups and two semi-finals, New Zealand losing by nine wickets to Pakistan in 1999.
"I want to keep playing but I'm standing down as captain of the one-day side," Fleming, who won 98 and lost 106 one-dayers as skipper, told reporters.
"I still want to captain the Test side," added Fleming, who became skipper in the longer format at the same time as taking over the reins in the one-day team.
"I've only just turned 34 and I think I've still got some good batting years ahead of me."
He added: "I want to concentrate on that for a while but I want to put a lot of energy into our Test cricket.
"I'd like to keep playing one-day cricket but as a batsman. In some way your energy levels are sapped when you captain the side.
"I want to play that