Counties Manukau Police arrested and charged the woman for the vandalism and damage of numerous graves at the Papakura Cemetery last month.
Inspector Mark Rowbottom said it was a relief to have made the arrest for the upsetting crimes that occurred on May 16.
"We had a team working full time on this case for weeks, and it's a great relief for them and for the families affected to have someone facing charges before the courts.
"The circumstances of the damage to the graves was devastating to so many families and we are pleased to have made this arrest for them.
"We'd also like to thank the community and the many members of the public who came forward to help us identify this person.
"We received a lot of support from numerous witnesses which was instrumental in making this arrest."
Reacting to the news this afternoon, Ms Bates said she was relieved but surprised police had made an arrest.
"I didn't think they'd actually be able to find the person, and I'm very surprised it was a female," she said.
"Obviously [they have] got no morals or motherly instincts in them, to do that to babies' graves -- I can't quite understand how someone could do it."
Ms Bates said the person arrested could benefit from being caught.
"They will be able to get the help they need because they're obviously not right."
Ms Bates praised police for their efforts.
"The police have done a really good job with what little information they had ... I'm a little bit happy, relieved, everything really."
Mr Rowbottom said he could not talk about the woman's motivations or the exact details of how police made their arrest because the woman was now before the courts.
But he did say "a culmination" of factors had led to the woman's arrest.
Public interest and media coverage helped police identify a range of suspects, he said.
"That first couple of weeks, with the information coming in from members of the public and the media putting it out there so much, it all culminated in people of interest being spoken to and then narrowing it down ... and eventually catching up to those people, which we have done and got that result."
Auckland Council said it was pleased to hear of the arrest.
Auckland cemeteries manager Catherine Moore said she welcomed the news, "which will be of great comfort to the families involved".
"The council would like to thank the police for their efforts and their support of our staff and the families following this distressing incident."
The council was not able to immediately comment on how much the clean up had cost.
A council spokeswoman said now the case was before the courts the council was unlikely to comment about seeking reparations for the cost of the clean up.
