The power outage hit the 227sq m rocky island - which lies south of Sweden in the Baltic Sea and has a population of nearly 40,000 - shortly before 8am (7am UK time).
The incident comes after two Russian-built gas pipelines in the Baltic Sea were damaged last month by blasts Denmark and Sweden suspected were intentional - though the reason for Monday’s outage has not yet been established.
Energy firm Trefor, which provides Bornholm with power, said on Monday the island was "unfortunately affected by operational disruptions”.
"There is no reason to speculate as to the cause at this time,” the provider said on its website, “and we are in the process of clarifying what is to blame for the power cut.”
Trefor added that one third of the island’s population had electricity back by 9.35 am (8.35am UK time) and power was expected to be restored to the whole island by midday.
Energinet, a public company that owns the sea cable that provides electricity to Bornholm, said a fault in the high-voltage grid resulted in electricity consumers on Bornholm losing power and it was "working hard to locate the problem”.
The outage came after blasts last month damaged two Russian-built natural gas pipelines in the Baltic Sea - two leaks were reported off Sweden and two off Denmark. All were in international waters.
The leaks from the Nord Stream 1 and 2 pipelines discharged huge amounts of methane into the air.
The governments of Denmark and Sweden previously said they suspected that several hundred pounds of explosives were involved in carrying out a deliberate act of sabotage.
However Russia dismissed suggestions it had attacked its own pipelines as “predictable and stupid”.
