The Carlton batsman was due to captain the side in the absence of Kyle Coetzer, who misses out as a result of county commitments.
However, Mommsen was injured during his side's Eastern Premier match with Watsonians on Saturday and the national side will be led instead by Sussex's Matt Machan. It will be his first match as captain.
"It's a huge blow for me - an initial scan has revealed a fracture and I've to see a specialist later this week to discover the full extent of the injury," said Mommsen.
The selectors have named a total of 15 players for the three fixtures which mark the start of Scotland's build-up for the World Cup next year. Freddie Coleman, Rob Taylor and Calum MacLeod will play in one match each due to county duty but Northants wicket-keeper David Murphy is available for all three fixtures after recovering from a hand injury. George Munsey, the Grange batsman, has also been included for the first time after impressing in last week's trial matches.
"After a block of squad training through July and Scotland trials last week, players are eager to get back into playing mode this week against a very strong New Zealand side," said Grant Bradburn, the Scotland coach who was formerly in charge of New Zealand. "With precious few opportunities remaining this summer, this series and the Ireland series in September will serve as important opportunities for players to confirm their skills at international level.
"It will be nice to catch up with some familiar faces in the NZA side. Their team contains a number of Test players and they have put in some really strong performances against England Lions and Sri Lanka A during their tour down south. It is going to be a big challenge for our players."
Scotland Squad (v New Zealand A. 15, 17, 21 Aug): M Machan capt, H Gardiner, C Wallace, G Munsey, R Berrington, J Davey, M Leask, M Haq, D Murphy, S Sharif, I Wardlaw, A Evans, F Coleman (2nd game only), R Taylor (3rd game only, C MacLeod (3rd game only)