The Bureau of Meteorology said the storm started around Geelong at about 12.30am before making its way to the city between 1am and 2am.

"We got quite a decent line of storms in the early morning," senior forecaster Dean Stewart said.

"But it was mostly noise with only about 0.4 millimetres of rain in the city."

He said the most rain fell in Greensborough, where about 3 millimetres was recorded overnight.

There is still a risk of isolated storms later in the day, with passing showers likely in the afternoon and a top of 22 degrees.

The lightning may also have sparked a fire in a rubbish dump at Somerton, in Melbourne's outer north.

Humans weren't the only ones to wake in fear, with spooked dogs reported missing to the Lort Smith Animal Hospital in North Melbourne.

"We've had several calls already this morning regarding lost dogs," head veterinarian Dr Andrew Kapsis said.

"Some animals may have escaped due to the frightening noise, and they'll hopefully start being taken in to local pounds or councils if people find them," he said.

"This highlights the need for pets to be microchipped so that people can be quickly reunited with their lost dogs and cats."

The RSPCA also reported a "significant" increase in the amount of dogs it had received due to the storm.

Powercor and CitiPower listed power outages in South Yarra, Bamganie and Meredith due to lightning strikes.

Strikes also caused traffic light outages in Chelsea, Aspendale, Rowville, Edithvale, Kew, Oakleigh and St Albans.

Lightning strikes are believed to have sparked the fire in a rubbish dump behind printer cartridge recycling centre Close the Loop at Somerton.

Firefighters were called to the 10-metre high blaze off the Hume Highway at about 2.30am.

About 100 firefighters and a water-bombing helicopter have been involved in the effort to bring the rubbish dump blaze under control.

Country Fire Authority duty officer Lachlan Redman said the dump contained a range of rubbish including building material.

"Due to the type of fire this is, it's likely to burn all day – if not for several days," he said.

"We've issued a Watch and Act message to the local community due to the amount of smoke issuing from the fire.

"We're advising people in the area to immediately close windows and switch off any external ventilation such as air conditioning."

Thick smoke forced the closure of Hume Highway between Somerton Road and Patullos Lane, as well as a section on Sydney Road, and impacted on homes and businesses in the area.

Calls to the recycling centre were not answered.

A woman who answered the phone at La Mirage Reception and Convention Centre next door said the venue was likely to be evacuated.

The CFA said it hadn't advised any nearby businesses or homes to evacuate.

Workers at the Somerton Truck Wash Express, across the Hume Highway and Sydney Road on Stanley Drive, are being told to go home.

"Because we've got the road blocked, not a truck can get down here to get washed," manager Darryl Pearson said.

"I'm about to tell the boys to pack up and go home. We've got nothing to do."

He said much of the smoke had cleared since he got to work at 6.30am, and they were "lucky" the wind was heading in the opposite direction.

"It was pretty bad," Mr Pearson said of the morning's smoke. "You could see it from five kilometres away at least."

The CFA and Environment Protection Agency are undertaking atmospheric monitoring at the site.

The cause is being investigated.