Anderson was eyeing a place in history on the third day of the third Test after taking the first six wickets to fall as New Zealand collapsed to 96 for six in reply to England's first innings 364.
But his quest for cricketing immortality was put on hold as rain and bad light prevented the third day's play starting as scheduled at 11:00am local time (1000GMT).
The 25-year-old Lancashire quick's figures of six wickets for 42 runs in 15 overs were already his best in Test cricket and they left New Zealand 69 runs short of avoiding the follow-on with all their top order back in the pavilion.
New Zealand, further bad weather permitting, now face a tough task in preventing England taking this series 2-0 after the hosts won by six wickets at Old Trafford following the drawn first Test at Lord's.
Debutant wicket-keeper Gareth Hopkins will resume on 11 not out with captain Daniel Vettori unbeaten on three.
England off-spinner Jim Laker was the first man to take all 10 wickets in a Test innings when he claimed 10 for 53 against Australia at Old Trafford in 1956. In the same game, Laker also took a Test record 19 for 90 in the match.
India leg-spinner Anil Kumble joined Laker in the record books by taking 10 for 74 against Pakistan at Delhi in 1999.
Back in 1896, England medium-pacer George Lohmann took nine for 28 against South Africa at Johannesburg.
More recently, New Zealand fast bowling great Sir Richard Hadlee took nine for 52 against Australia at Brisbane in 1985 - an innings where the all-rounder caught Geoff Lawson off Vaughan Brown to give the spinner his only Test wicket.