Although the event was "very scary", the pilot assured the passengers the plane was built to handle such strikes.
"I was still relieved when the plane landed about five minutes later."
An Air New Zealand spokeswoman said the plane would be checked by engineers. The plane's scheduled departure from Dunedin yesterday was cancelled, and passengers were put on other flights, the spokeswoman said.
"Lightning strikes are not uncommon and aircraft are designed with this in mind."
MetService meteorologist James Millward said the plane strike was one of about 50 lightning strikes near Dunedin on Saturday.
Two "bursts" happened about 1pm and 5pm, Millward said.
During the storm, 12mm of rain fell in the Dunedin city centre, and 7mm at Dunedin Airport.
The extreme weather, caused by cold air and a weak frontal feature, also disrupted lights at Forsyth Barr Stadium during the rugby clash between Otago and Southland.
A witness said the stadium was left in partial darkness and nothing could be heard over the roar of rain on the stadium roof.
Forsyth Barr spokeswoman Kim Barnes said the stadium experienced a power surge because of a lightning strike elsewhere in the city.
"Fortunately, due to an earlier kick-off time of 5.05pm, there was still good natural light along with reduced lighting to ensure play could continue without interruption."
A police spokeswoman said a two-vehicle crash on the Kilmog, near Dunedin, occurred during a period of "severe hail" about 2.20pm.
Police could not confirm if the hail was the cause, the spokeswoman said.
No-one was injured in the crash.
Dunedin residents also reported brief power outages during the storm.