The Pakistan all-rounder plays for the King's XI Punjab in the Indian Premier League but the team did not qualify.
There are six teams in the qualifying tournament. Two will qualify for the main draw which starts on October 13.
The former Pakistan Test and ODI team member is settled in England and has a British passport.
He plays for Kent in the English county but also plies his trade in other Twenty20 leagues.
He had had featured in the Sri Lanka Premier League as well. Mahmood picked a wicket and scored 24 in the first game against Sialkot Stallions of Pakistan on Monday, which the New Zealand side won by six wickets.
Hampshire opener Michael Carberry (65) played a lone hand as Sean Ervine's 16 was the next best score.
Mahmood struck twice in the fourth over to cause early damage and then dismissed his former Pakistan team mate Shahid Afridi in his next over.
Afridi failed to score as his horror run with the bat continued. Mahmood also struck twice in the 19th over to dash any hopes of a final push to the Hampshire score.
The qualifying pool 2 features Trinidad and Tobago, Yorkshire as well Uva Next, the Sri Lanka Premier League champions.
Brief Scores: Hampshire 121/8 in 20 overs (M Carberry 65, A Mahmood 5/24); Auckland 123/2 in 14.3 overs (A Mahmood 55 no)