Energy Minister Eli Cohen said power was briefly disrupted, with electricity restored to most of those who were affected.
"The damage to the power grid in the north is localised and not significant," Cohen said.
"Also, in the barrage towards the north, there was no significant damage to Israeli infrastructure sites."
Iran's Islamic Revolutionary Guard Corps said it had targeted refineries in Haifa, Israel's third-largest city, and in Ashdod, in the country's south, "along with a range of security targets and military support centres of the Zionist regime" which it said "were hit by pinpoint missiles".
There was no immediate word on whether the Ashdod refinery was hit.
Police said bomb disposal units were at several sites in Haifa where munitions landed.
No casualties were reported.
Israel's Ministry of Environmental Protection said debris from a missile that was intercepted fell in Haifa and was being examined as a hazardous materials incident.
Israel Electric Corp said a power line in the Haifa area was hit by shrapnel, causing a brief outage, but that electricity was restored to all customers within about 45 minutes.
Last June, Oil Refineries in Haifa was hit by an Iranian missile, which killed three people and halted operations.
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