It was too soon to comment on what, if any, changes needed to be made around keeping the public safe in parks containing livestock.
"Auckland Council and Panuku Development Auckland are currently investigating and reviewing what happened, and as part of this we will be considering any changes that may need to be made.
"The grazier, who has informed WorkSafe, is assisting us with the review," the spokesman said in a statement.
Worksafe confirmed it was not investigating the incident as it did not happen at a workplace.
Manurewa Local Board chairwoman Andrea Dalton earlier told the Herald the board had already been discussing fencing off all of the tracks from livestock to stop cows trampling and destroying them.
The council spokesman said their focus at the moment was "the safety of the public using the park and the wellbeing of the members of the public involved in the incident".
"We have been in contact with the woman involved in the incident, and we are still trying to contact the man. We will continue to check on them, and we wish them both speedy recoveries."
About 60ha of Totara Park contains an area grazed under licence, which was also accessible to the public.
"The areas under grazing at the park are fenced into paddocks and accessed through gates at the public's discretion."
Panuku manages 12 grazing licences, including at Totara Park, over approximately 200ha, the majority of which is part of the council's park network.
"Grazing enables cost-effective vegetation management, while at the same time we work to provide suitable guidelines around stock management and animal husbandry.
"Livestock grazing also provides a revenue stream through providing grazing licences and sale of animal products. This also helps with pasture control.
"We do this in an efficient and cost-effective manner that optimises the economic return to the council without compromising the role and purpose of our parks."