It is just the second time a New Zealander has occupied the top spot, following Glenn Turner in 1979.
Mitchell replaces Rohit Sharma of India after scoring his seventh ODI century against West Indies in Christchurch on Sunday.
He climbed two spots. Sharma is now second and Ibrahim Zadran of Afghanistan third.
Mitchell was injured in the Christchurch game and will miss the rest of the ODI series.
Rachin Ravindra is the next-highest New Zealand batter, at 13 in the ODI rankings.
Meanwhile, Jacob Duffy, who was the top wicket-taker in the T20 series against West Indies, has moved up to number two in the T20 bowling rankings.
India's Varun Chakaravarthy remains number one.
New Zealand is number two in the ODI team rankings, fourth in T20 rankings and fifth in the test rankings.
