The band, which has been performing in New Zealand and Australia, will play a gig in Dunedin next weekend, and turn up at the University of Otago for a public discussion.
Pussy Riot has stayed longer than expected after a visa problem meant a planned trip to Brazil was cancelled.
The feminist group has made headlines worldwide with its activism and anti-Vladimir Putin stance, which has led to members being jailed in the past.
The band will perform at Dunedin brewery New New New on March 17.
New New New spokeswoman Dallas Synnott said she was contacted by a local musician who had been contacted by Pussy Riot.
"They decided they love New Zealand," Ms Synnott said.
"They just decided to stay a lot longer and do as many shows as they could while they were here."
Ms Synnott said the prospect of the visit was "very exciting".
"I'm thrilled to do this show.
"I've been reading about them for years now, and I think this is a pretty momentous gig to come through Dunedin."
It was appropriate for the band to come now as many people in Dunedin were interested in international politics and "quite like the cut of their jib, frankly".
"They're extremely brave, extremely pioneering and empowered."
A day before the gig, members of the band will attend a public event at the University of Otago's department of media, film and communication studies.
"Art, Protest & Power: In Conversation With Pussy Riot" will be "a conversation on the power of art, spectacle and transgression in these chaotic, media-saturated times".
A film about the band, Act & Punishment, will be shown, followed by a discussion.
Eight members of the band are understood to be attending.
Lecturer Rosemary Overell said her department considered how media worked in terms of socio-cultural politics.
"We're interested in how Pussy Riot have used various forms of media to talk back, or present a counter-discourse to patriarchy.
"They're one of the most significant global feminist groups at the moment.
"It's almost going back to 1970s types of feminist political performance, disruption of public space."
She said that varied from the "commodified" feminism presented by the likes of American performer Beyonce.
"Pussy Riot are doing something almost more extreme."
