Tui, an Olympic silver medalist, could be ruled out given the usual recovery time ranges anywhere from one week to a month.
The sevens competition starts on April 13 for women and a day later for men. The finals are on April 15.
Tui's sickness continues an injury and illness plagued build-up for the men's and women's teams.
On Tuesday it was announced Kat Whata-Simpkins suffered a leg injury and would miss the Games.
Tenika Willison was promoted into the squad of 12 and Alena Saili joined the team as the travelling reserve.
The news wasn't any better for the men after emergency appendix surgery removed Blues teenager Caleb Clarke from contention.
Clarke's illness came after playmaker Ngarohi McGarvey-Black was forced to return home. He injured his ankle in a warm-up match against Australia.
Etene Nanai-Seturo flew to the Gold Coast as a replacement on Sunday.
"His ankle injury wasn't too serious, but it wasn't going to come right in two weeks," New Zealand men's coach Clark Laidlaw said.
"Etene was the obvious choice, because it had already been one of the tightest calls [to leave him out]."
"He was on our 'long list' of players already accredited, because rugby is such a moving feast."
While the women debut at this Commonwealth Games, the men have a pedigree of four golds and a silver to uphold.
Without the customary quarter-finals of the world series events, the pressure will be immediate.
Four of the teams – New Zealand, South Africa, Australia and Fiji (two) – have won tournaments this season.
Ten of the world's top 13 sides are represented on the Gold Coast.
"There are not many events at the Games where so many teams have a genuine medal opportunity," Laidlaw said.
"We're under no illusions how tough it'll be to get out of our group."
Kenya finished second at the most recent leg in Vancouver, where New Zealand bowed out in the quarter-finals.
Canada came fourth in the tournament New Zealand won at Cape Town in December.
The Kiwis' other pool opponent is Zambia.
