"All I can say is that Tarn's is once again showing us what an incredible battler she is and, right now, she is putting up the fight of her life.
"We couldn't be prouder of her or love her more."
The family said there had been an amazing outpouring of love and support, which they appreciated. They asked for space to focus on caring for her.
Former Silver Ferns coach Yvonne Willering said: "[The news] came as a complete shock. I'm looking for positive outcomes. I think this is a time for family and people like us, all we can do is care and show support."
Tania Dalton was treated on the field at Northcote's Onewa Domain, bleeding profusely from the mouth and nose.
Her injuries did not come from any impact during the game, she was running when she collapsed.
She starred for the Silver Ferns during 37 tests, playing at goal shoot and goal attack from 1996-2007, but missed the 2005 campaign through injury.
Tania Dalton is now a Sky TV commentator, and has been involved with the Takapuna Rugby Football Club, where her children play, for several years and plays in a social touch rugby team on Thursdays.
Club chairman Simon Cheesman said the former Silver Fern was playing for her Pita Pit team when she suffered a "medical emergency".
He wasn't at the grounds, but was told no impact was involved. "She was just on her own, she was running."
Her husband, Duane Dalton, a Pita Pit NZ director, was called to the ground, Cheesman said.
He said "everyone helped" after Tania Dalton's collapse, including a medical student playing on another team.
"The games were all stopped."
"Obviously we are extremely concerned ... I know her very well. She's a neat mum and a lovely person," Cheesman said.
Tania Dalton was part of the 2003 Netball World Championship-winning side in Kingston, Jamaica and was part of the team that finished runners-up at Christchurch in 1999.
She was also in the 2002 Southern Sting squad which claimed the national title.
Tania Dalton retired from international netball in 2007 to concentrate on family, but was persuaded to make brief comebacks in elite trans-Tasman tournament, the ANZ Championship, in 2008 and 2011 playing for the Southern Steel.
Willering described Takapuna-born and raised Tania Dalton, who retired from netball in 2011 to concentrate on her family, as a "loyal North Shore girl", even when she was playing for teams outside the city.
"Her heart was still with the Shore. I loved that about her. She's just a wonderful person and very positive. I just want to carry that on, and she would want us to be positive, too."
As well as raising her family, Tania Dalton has given her time to community volunteer work, including judging local sports awards.
She has also carved out a successful business career as part-owner in Pita Pit, a popular food franchise.
Since her playing career ended, she has become a regular on TV screens as a well-regarded commentator on the trans-Tasman netball championship.
SKY TV spokeswoman Kirsty Way said the company was aware of Tania Dalton's medical emergency.
"All of her Sky crew are wishing her all the best for a quick recovery."