While winds are expected to ease this morning, rain could mar the rest of the week, MetService said.
A Fire and Emergency New Zealand spokesman said crews were called to reports of a house with loose roofing iron in Wakari Rd, Helensburgh about 8.50am yesterday.
Firefighters also attended a similar incident in Dover St, Liberton, about 12.30pm, he said.
In both cases firefighters helped reattach the roof.
About 9.30am, firefighters assisted to remove a conservatory which had blown over at a Centennial Ave address in Helensburgh, the spokesman said.
The Dunedin Botanic Garden was closed for the day after strong winds caused fallen trees and branches.
A statement posted to social media by the garden apologised for any inconvenience and said it hoped to reopen the gardens as normal today.
A MetService metrologist said there was a slow-moving low sitting to the west of New Zealand and a ridge off to the east of the country.
New Zealand was being squeezed between the two meteorological features, causing strong north-easterly winds in many places.
The winds around Dunedin were expected to ease this morning, but morning rain was likely today.
Isolated showers were expected for tomorrow and Wednesday, with rain and easterlies likely on Thursday.
There was a low risk that heavy rain could fall later this week, the metrologist said.
