The 18-year-old, who is the son of former New Zealand opener Craig Cumming, will take his place in the side alongside Otago players Jarrod McKay and Mitch Renwick.
The left-handed opener is in the wider Otago squad and is expected to make his debut at some stage this season.
Jacob Cumming impressed for Otago A last season, scoring 306 runs at an average of 38.25, and is highly regarded.
Volts coach Dion Ebrahim said he was a player on the rise.
"Everything I’ve seen and heard of Jacob has been very impressive," he said.
"We included Jacob in our pre-season camps with the view of keeping him closely connected with the Volts with the long-term view of him potentially playing at some stage this season.
"What has really impressed me is the time that he has at the crease. Nothing seems to faze him in regards to pace.
"Normally, you see young batsmen of a school age struggle on the back foot. But Jacob looks like he has an outstanding technique and, from everything I’ve seen, a very sound temperament as well."
Cumming has also been selected in a New Zealand development team which will tour the country next year.
The New Zealand XI includes Black Caps stars Neil Wagner and Devon Conway.
The game gets under way on December 28 and will be played on Bay Oval’s No 2 ground.
Conway and Wagner have been selected in the side to get some much-needed cricket under their belt ahead of the test series against Bangladesh, starting on January 1 at Bay Oval.
Conway has been sidelined since he broke a bone in his hand during the ICC T20
World Cup semifinal against England in November.
His selection is subject to being fully recovered in time to take the field.
“I’m really looking forward to getting back into some competitive cricket and hopefully I’m passed fit to play,” Conway said.
“I’ve just started batting again and testing out my hand, so I’m hopeful of making my return for the New Zealand XI. There’s nothing like a match situation to really test it out and help build some confidence.”
New Zealand XI selector Gavin Larsen said the fixture was important for Conway and Wagner, but also a chance for promising domestic talent to test themselves against international cricketers.
Wellington Firebirds batter Tim Robinson and Cumming are two who have shown promise at age-group level.
“Both Tim and Jacob are emerging talents and have already made promising starts to their cricketing careers," Larsen said.
" I know they will both relish the chance to play for the New Zealand XI and show people what they’ve got.”
Brendon Donkers will coach the New Zealand XI for the two-day warm-up fixture.
New Zealand XI
To play Bangladesh
Ma’ara Ave, Jakob Bhula, Jack Boyle, Devon Conway, Jacob Cumming, Joey Field, Jarrod McKay, Tim Pringle, Brett Randell, Mitch Renwick, Tim Robinson, Neil Wagner.
