The 22-year-old will be replaced by Tauranga's Amy Robinson, who has played 45 tests for New Zealand.
''I'm hugely disappointed for Tessa as she has been training and playing well in the lead-up to the Commonwealth Games, but I fully support the decision that the medical team has made,'' head coach Mark Hager said.
''Our top priority is Tessa's welfare and we ask for people to please respect her privacy on this matter.
''We look forward to welcoming Amy to the team and seeing what she can deliver come Games time.''
Jopp shifted to Auckland three years ago to further her hockey but hails from Kokonga, where her family owns a farm.
She followed in the footsteps of players such as Shane Collins and Mandy Smith, who also came from Maniototo and went on to play for New Zealand.
No details of the medical reasons were offered.
The New Zealand women's team opens its campaign against Scotland next Thursday.
