Vettori is likely to miss the Black Caps' next match against England A as a precaution after he finished day two of the match at Chelmsford with a nasty cut to the index finger of his bowling hand.
The spinner sustained the injury to his left hand while fielding but, although the stitches are likely to be in place for between seven and nine days, he should be fit for the first test against England starting at Lords on May 15.
New Zealand were all out for 355 when Ryan ten Doeschate had Michael Mason lbw with his first ball to finish off a troublesome last-wicket stand.
Essex's reply was led by England batsman Ravi Bopara who hit 66 as his county reached 251-9 at the close.
There was good news for England as opener Alastair Cook proved his fitness. Cook batted without discomfort from the right little finger he dislocated on Friday during his 31-ball innings before being dismissed by Mason for 15.