Dalziel has held the mayoralty for three terms, being first elected in 2013.
Her husband Rob Davidson died last year.
Announcing her decision, she said it had been an absolute privilege to represent the city where she was born and lived all her life.
"People see the 'politics' of the council table played out in the media. Trying to manage that environment, however, is only one part of the role. There is also a civic leadership role that has called on me to both represent and speak for the city. That is the privilege.
"I have thoroughly enjoyed representing the city at civic events, citizenship ceremonies, and I have welcomed delegates to national and international conferences here in Ōtautahi Christchurch. On each occasion, it is the office of Mayor and the honour of the city that I have upheld," Dalziel said in a statement.
She said she was deeply proud of the relationships built across the region, particularly with mana whenua.
"We have connected with Te Rūnanga o Ngai Tahu and developed relationships with the six Papatipu Rūnanga... Establishing a committee of the chairs has been an important step in the relationship. We have further to go, but the foundations are there."
"If we have learned anything from our experience over the past decade, it is that true collaboration is the only way to achieve the best results."
She reflected on the challenges the city had faced during her tenure.
"I won't go through all the financial challenges we inherited, other than to remind people it started with a $400 million hole in the budget and the loss of accreditation to issue building consents in the biggest rebuild the country has ever faced.
"We then had the floods. The Mayoral Taskforce we established in response has guided us as we have systematically tackled each element of the vulnerabilities we were exposed to. It was extremely gratifying seeing no homes flooded in the recent event - it has been a big investment, but it is paying off.
"The Port Hills Fires were also tragic, reminding us of the dangers that come with residential proximity to rural environments.
"Being mayor at the time of the mosque shootings and standing alongside our Muslim communities was devastating, but also uplifting. The incredible Muslim leaders who spoke of unity, peace and compassion, as well as offering forgiveness, were incredibly moving.
"The response of our community, measured each morning as the tribute wall grew, became the backdrop to the international news interviews we did every morning. The thousands who turned up at the Call to Prayer one week later sent a powerful message to the Muslim community - 'we have got your back'."
"But we still have issues in our city. There is more to be done. We are not all as inclusive of diversity as most of us want us to be. I want to start a conversation about that before I leave office."
She thanked her council colleagues and staff, and those who wanted her to run again.
"The reality is the one person that I need by my side to do that, my husband Rob who died last year, has gone.
"It is time for a new direction in my life. I don't know where this will lead, but I will always be proud of what has been achieved, and the firm foundation for the future that we have built together."
