Once the most expensive seats have gone, fans will have to fork out $699 or $998.99 for a package, which includes a seat and exclusive memorabilia.
Frontier Touring New Zealand spokesman Brent Eccles said the morning sales period was "crazy" and a lot had gone "within the first half an hour".
Mr Eccles wouldn't say how many of the tickets bought fell into the lucky dip category. They were promoted as a way for fans to see the concert at a relatively cut-price $99.
One person trying to buy tickets said they appeared to have gone by 9.05am.
Mr Eccles said the lucky dip tickets could be anywhere in the stadium, from general admission to the best reserve seats.
He said ticket sale patterns were similar to those for the first of two Bruce Springsteen shows at the same venue next March.
"[But] I think Springsteen may have sold a bit faster."
While there was only one listing for Rolling Stones tickets on Trade Me last night, there were dozens for Springsteen's two shows.
The Stones are playing six dates in Australia before finishing the Australasian leg of their tour in New Zealand.