The mayor applied for two months leave but the council decided to grant six months to give him as much space and time as he needs to recover fully.
Councillors acknowledge Mr Brown may return earlier.
The council has granted leaves of absence to councillors in the past for a variety of reasons.
Acting mayor Gary Troup will continue in the role until Mr Brown returns.
“None of us know when Len will be able to resume his mayoral duties. That depends on his progress and medical advice,” Mr Troup says.
“But we all hope Len’s recovery goes smoothly and that he is restored to full health.
“In the meantime I will continue to work as hard as I can for the good of the city.
“I have had tremendous support from councillors and the community since I have been acting mayor. I greatly appreciate that support.”
Mr Brown is in a stable condition in Auckland Hospital.