Ukrainian electricity company Ukrenergo said a pylon had come down and it was investigating the cause.
Russian forces annexed Crimea from Ukraine in March 2014, but the peninsula remains largely dependent on Ukraine for electricity.
The current disruption is not thought to be as serious as November's outage.
Crimea's two million people were severely affected when four pylons on the Kakhovsky-Titan power line were intentionally damaged on 22 November. It took more than a fortnight for supplies to be restored.
Until recently Ukraine provided Crimea with 70% of its power, but Russia is now trying to boost electricity supplies to the peninsula.
Moscow officials says two power lines through the Kerch Strait began providing 400 megawatts of electricity to Ukraine this month and further supplies will begin in May 2016.
The issue of energy supplies between Russia and Ukraine has become intensely politicised since Ukraine's pro-Russian President Viktor Yanukovych was deposed in February 2014.
A contract between Ukrenergo and Crimea was set to come to an end on Thursday and there was no indication that it was being renewed in time for the new year.
A free trade agreement between Ukraine and the EU, due to come into force on 1 January, has also added tensions in the region.
No power at all was flowing from Ukraine to Crimea on Thursday, and officials on the annexed peninsula were planning to phase in rotating power cuts ahead of the Russian New Year holiday.
"I am asking people of Crimea not to worry. The Crimean authorities have the situation completely under control," Crimean leader Sergei Aksyonov wrote on his Facebook page.
"We have not been relying on Ukrainian electricity and we are not relying on it now."
Ukrenergo spokesman Zynoviy Butsyo told Ukrainian TV that a pylon had come down some 20km (12 miles) from Kakhovka, to the north of Crimea, and officials were trying to work out how long repairs would take.
Crimean Tatar activist Lenur Islyamov suggested that strong winds might have brought down the pylon and denied that Tatar activists had been behind the latest power cut.
Electricity supplies to Crimea from southern Ukraine have been cut, weeks after power lines were sabotaged apparently by anti-Russian activists.