The city centre "experienced a large power cut around 11.00 am (1000 GMT) after an electricity cable was cut during excavations" just south of Amsterdam's historical canal belt, Liander announced on its website.
"Some 28,000 households are without power," it said.
Amsterdam's famous Rijksmuseum was evacuated and will remain closed together with the nearby Alard Pierson Museum, news reports added.
Elsewhere on the city's famous Museum Square, the Van Gogh and Stedelijk Museum of modern art however remain open to the public, Dutch public broadcaster NOS reported.
Bystanders at the Rijksmuseum posted images on Twitter of a heavy police presence at the museum, which has priceless artworks such as Rembrandt's famous 17th century painting The Night Watch.
Elsewhere, pedestrians tweeted pictures of lines of stationary Amsterdam trams with one person saying "Line of trams from the Spui to Dam Square... no ordinary sight."
Many shops have also closed up and those open were only doing cash transactions, the NOS added.
Liander said its technicians "are working to restore power, but we cannot say how long this may still take."
The Dutch capital attracts some 17 million tourists per year and many of them visit Amsterdam's central and historic canal belt and famous red-light district.