The 22-year-old Jacobs was taken by Mumbai for the base rate of 30 lakh (US$35,000), though he has played only nine domestic T20 matches with a highest score in six innings of 42 in 20 balls.
The hard-hitting right-hander has found a role as a finisher in T20 matches for Canterbury province initially and now for Auckland.
"He's a promising player with a lot of talent and we're looking forward to exposing him to international cricket," New Zealand selector Sam Wells said. "He's clearly got a lot of power with the bat, but he's also shown in the longer formats that he has a decent technique and temperament."
Jacobs was named Monday in a 13-man squad which will be captained by Mitchell Santner.
Also included are Mitch Hay, Zak Foulkes and Tim Robinson who made their New Zealand debuts in Sri Lanka earlier this year but have yet to play an international at home.
Jacobs, Foulkes and Robinson have not been named in the New Zealand squad for the three-match one-day series against Sri Lanka which follows the T20 series. The first T20 match will be played at Mount Maunganui on Saturday.
Kane Williamson and Devon Conway have not been named because they have opted out of New Zealand Cricket contracts to play in overseas T20 leagues, as have Adam Milne, Finn Allen and Lockie Ferguson who are playing in the Australian Big Bash League.
New Zealand T20 squad: Mitchell Santner (captain), Michael Bracewell, Mark Chapman, Jacob Duffy, Zak Foulkes, Mitch Hay, Matt Henry, Bevon Jacobs, Daryl Mitchell, Glenn Phillips, Rachin Ravindra, Tim Robinson, Nathan Smith.
New Zealand ODI squad: Mitchell Santner (captain), Michael Bracewell, Mark Chapman, Jacob Duffy, Mitch Hay, Matt Henry, Tom Latham, Daryl Mitchell, Will O'Rourke, Glenn Phillips, Rachin Ravindra, Nathan Smith, Will Young.
