The Basin Reserve Trust has struggled to find a naming sponsor for some time.
City councillor Fleur Fitzsimmons, who is a Basin Reserve Trustee and holds the recreation and community facilities portfolios, said she supported the campaign.
"We will be sending an important message to girls and women across the world that in Wellington we value the role of women in sport," she said.
"I want all girls to feel valued when playing sport at whatever level. We have more work to do to ensure equal pay for women and men in sport and much more to do around promotion of women athletes and women's sport, but renaming our premier test cricket ground to support women's sport is an important symbol."
Mayor Justin Lester said the initiative was brilliant and one everyone should support.
"I look forward to the day when our daughters can achieve the same level of personal and financial success in their chosen sport as our sons," he said. "I look forward to them achieving equal pay and recognition, and the support they deserve."
Sports Minister Grant Robertson said: "Visibility is one of the three themes of our Women and Girls in Sport Strategy, and there is not many places more visible than the Basin Reserve.
"More opportunities for women and girls to participate, compete and suceed in sport is good for our future as a fair and healthy country"
If more than $100,000 is raised in the campaign, Support Women's Sport would look to extend the time period of any naming rights it secured.
The campaign will launch tonight and run over 17 days.