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The television veteran is understood to have found out last Friday that he would need an operation.
Close family friend Leanne McGoldrick said the operation was to remove the tumour but treatment would be ongoing. She said the family had asked for privacy.
"He has come through the surgery well.
"It's a difficult time for the family as they come to terms with the news of his brain tumour and the options for treatment.
"We would appreciate it if the family's privacy can be respected during these early stages. We will be in a better position to comment publicly once we have more details from the specialists and a better understanding of the right course of action.''
A broadcaster since 1970, Leishman has been a longtime fixture of New Zealand's television landscape.
Most recently he has hosted the Golf Show, but has also covered Olympic and Commonwealth Games for TVNZ, as well as yachting, tennis, league and rugby.
He was also the host of Wheel of Fortune, the country's longest-running television game show and has been a longtime supporter of children's charity Variety.
His brother Mark Leishman is a radio host.
- Yvonne Tahana of the NZ Herald