Nine others were rescued in the incident at Lake Tekapo, a popular tourist destination.
Those rescued are suffering from hypothermia and some have been taken to hospital, police said in a statement.
All of the group were wearing life jackets.
The identities of the victims have not been released but local media has reported that the two dead are men in their 20s.
Police Inspector Dave Gaskin, the mid-south Canterbury area commander, told Radio New Zealand that the kayaks were "swamped" after a sudden weather change.
The temperature in the lake was about 3C, and it would have been even colder with the winds, he said, according to the New Zealand Herald.
Police say an investigation will take place into the incident.
In October 2009, three men drowned on the lake after crashing their boat into what was thought to be a log.
Two foreign tourists have died while kayaking on a lake in New Zealand's South Island after being hit by strong winds that tipped them into the cold water.