A police spokesperson said the driving behaviour has "adversely impacted" some animals, as well as causing significant stress to staff at the park.
"There is also an extreme fire risk posed by this activity that could have potentially devastating effects on the park."
Police launched Operation Gumtree, targeting the "anti-social road user behaviour".
"The operation identified 16 vehicles involved in offending. Ten of the vehicles identified have already been impounded, and inquiries are under way to locate the remaining six vehicles."
Some of the vehicles had been identified as committing multiple offences – either on the same night or over several nights.
"The message for participants is clear: those involved can expect to be held accountable for their actions."
Orana Wildlife Park just outside Christchurch has been a family favourite since 1976.
Set just off McLeans Island Rd, it has giraffes, lions, gorillas, rhinos, meerkats and other endangered exotic and native species.
