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South Africa-born Elliott, 33, who played the last of his 37 ODIs more than two years ago, was called up after Anderson broke his left thumb after being struck on the hand while bowling.
Anderson, 22, played in all three Twenty20 internationals against South Africa in December and had been retained in the ODI squad for the three-match series this month before he was injured in a domestic match.
His thumb is in a cast for the next two weeks.
"We decided to replace him (Anderson) with another batting all-rounder in Grant Elliott," Black Caps coach Mike Hesson said.
"Grant comes into the squad with invaluable knowledge and experience of South African conditions."
Elliott last played for New Zealand in a one-day international against India in December 2010.
He averages 32.54 with the bat, scoring 115 against Australia in 2009, and has taken 19 wickets with the ball.