A TVNZ spokeswoman said Olsen's departure is not related to proposed changes to the broadcaster's newsrooms, which were announced to staff this week.
Head of news and current affairs John Gillespie said Olsen would be missed by both viewers and colleagues.
"Karen's knowledge as a meteorologist and her dedication to broadcasting has been top rate, we'd like to thank Karen for her service to New Zealand audiences and TVNZ."
Olsen, who has been with TVNZ for 22 years, will be on air until early November.
Contacted this morning about speculation her role was under review as part of a shake-up at the network, Olsen said she would "get in big trouble" if she commented.
"There's a lot of that happening. It's still a process that's ongoing ... I'm pretty sure it will all become clear in two or three days."
There is speculation that Renee Wright could take on weekend weather duties with Dan Corbett becoming a weekday staple.
The move comes as TVNZ has confirmed it has "entered into consultation with a small number of news and current affairs staff".
Mr Gillespie said the proposal would include changes to newsroom roles across New Zealand.
There would be "some possible staff redeployment" and "an estimated eight to 10 roles impacted".
He said the proposed changes are about TVNZ continuing to refine its news-gathering processes.
"Technology efficiencies and news-gathering changes mean we can, and have to, operate our business differently in order to continue to be successful.
"Our focus on credible journalism and delivering the moments that matter to New Zealanders on all platforms will not change," Mr Gillespie said.
TVNZ would not be commenting further until the proposed changes were confirmed.
It's understood that roles that could be disestablished include a Dunedin-based reporter, three camera operators and two directors of coverage.
When asked whether specific presenters and positions would be affected, TVNZ said: "TVNZ cannot comment on specifics relating to proposed newsroom changes at this point in time as we are in consultation with staff and the process is subject to change."
The announcement follows news earlier this week that Good Morning has been axed by the state broadcaster, affecting approximately 15 staff and contractors, including host Jeanette Thomas.