Gill, who only turned 19 in September, played for the Kolkata Knight Riders in the Indian Premier League this year on a contract worth US$280,000.
Also in the named squad is Manish Pandey who's played 23 ODIs and 28 T20 Internationals for the main India team.
With the Ford Trophy domestic 50-over competition finishing this weekend, the intrigue will be to see if the New Zealand selectors take account of form in that competition when picking the New Zealand A team.
Wellington's Andrew Fletcher has made 614 runs in his rookie season, including three centuries. But a failure yesterday for the Firebirds in the elimination final against Auckland won't have helped his chances.
New Zealand A lost all three 50-over matches to Pakistan A during their recent tour of the United Arab Emirates and will be keen to reverse that run of results at home.
Kelvin Jones is encouraging local fans to make the most of the late start and free admission to the games.
"We'd love to have people come along and set up their barbecue and enjoy some quality cricket hopefully on dry and warm nights next weekend."