There's surface flooding in the Central Otago town of Roxburgh and two slips of State Highway 8 between Roxburgh and Ettrick.
Diversions are in place at the Millers Flat Bridge and the Roxburgh Dam, police say.
NZTA says SH8 is closed on the northern side of the Roxburgh township.
Rain is continuing to fall and there is widespread surface flooding in the Roxburgh area, police say.
Blocked drains and gutters had caused flooding at the Roxburgh Area School, Teviot Valley Rest Home, the Roxburgh Bowling Club and one other property, the Otago Daily Times reports.
Earlier MetService warned thunderstorms may be severe in inland parts of New Zealand and flash floods were possible.
"What a thunderstorm can do to your day - weather trace from Roxburgh shows temperature falling almost five degrees in an hour while 30mm of rain falls," MetService tweeted.
Weatherwatch.co.nz said daytime heating plus converging winds had helped create significant downpours and thunderstorms around Otago on Sunday.
Central Otago and others areas had earlier been affected by a heatwave.