"I feel fit and well, and it's a miracle it got picked up."
Because of the early diagnosis, the Motukairangi/Eastern Ward councillor expects to be back at work by June.
He will take leave from Friday June 17 for treatment and recovery.
During this time, councillor Jenny Condie will fill his role as chair of the council's infrastructure committee.
Rush is also vacating his appointments on external trusts and committees, including the Basin Reserve Trust, Sky Stadium Trust and Wellington Water Committee, to focus on his treatment.
Wellington mayor Andy Foster said it was important that Rush focuses on his health and family right now.
"Sean is a valued member of the council, and we look forward to seeing him resume his rightful place around the decision-making table when he is ready."
Rush is thankful for the support shown by his council colleagues at this difficult time.
"I'll knock this off and be back to finish the triennium (the rest of his three-year term). In the meantime, I request privacy for me and my family so I can give this treatment its best shot."