The world heavyweight boxing champion successfully defended his title against Romanian Razvan Cojanu in Auckland.
Sky TV had warned that piracy teams would be on the lookout for illegal online streams.
"We took down many YouTube and Facebook streams," Sky TV director of corporate communication Kirsty Way told the New Zealand Herald.
"Around 10 people are likely to face court with the evidence we have."
Way said the monitoring team also found some illegal streams of the Fiji-Tonga rugby league match.
Sky said it had previously won 13 cases against those who illegally streamed Parker's fights.
They were fined up to $3000 each.
Parker had also urged people not to stream the fight before his first WBO world heavyweight boxing title defence.
"My message is don't do it because it is illegal for a reason, and if I catch you you're going to be in trouble," Parker said.
"I feel there's a lot of people working hard behind the scenes to get the fights going and showing things on TV...when you're doing that sort of stuff you're taking away from those that are working hard.
"Everyone has families that they have to feed and pay for and that's why I feel it shouldn't be done."
Sky chief executive John Fellet said illegal streaming was no different to "walking into a store and grabbing a physical item".
"It may be fun, it may be exciting, but at the end of the day you are taking money out of athletes, the actors and the production people and even people here in this building," Fellet said.
He said Sky would "fingerprint" the streaming signal to track back to who it goes to.
"Right now we are taking civil actions and using the courts to make our point," he said.
"In other countries around the world they take greater criminal action on these types of events."
