They hope that the fear of electrocution will deter so-called roof surfers, a big problem in the country.
The plan is one in a series of failed attempts to tackle unsafe riders.
But commuters say that ticket prices should be lowered instead – a rise of 40% is expected on 1 October.
State railway company Kereta Api Indonesia said it would start lowering the power lines on some tracks on Friday, to make the roof surfers think twice.
An official told the BBC that the railway authorities would take responsibility for any casualties, but did not elaborate further.
Officials have said that the practice of riding on roofs is extremely dangerous, with people falling off and at least 11 deaths reported in 2011.
Previous attempts to deter roof riders have included spraying the roofs with paint, spreading oil on carriages and hiring musicians to perform safety songs.
In January, concrete balls that delivered a severe blow to the head were even hung above train tracks, but this also proved to be ineffective.
Passengers can be seen on train roofs every morning and evening. At peak times about 400,000 commuters cram in or onto carriages travelling into and out of the centre of Jakarta