The plant was hit at 9:55 p.m. (1755 GMT) on Friday and was disconnected from the grid, Interfax news agency cited the ministry of territorial administration and infrastructure as saying.
According to Reuters, the plant, about 25 km (15 miles) outside the capital Yerevan, is supervised by the Armenian government.
"The reason was a lightning strike, which caused the station's safety systems to switch it into safe shutdown mode," it said.
The ministry said personnel were working to restart the plant, according to Interfax.
SD/