One of the points at Raxaul-Birgunj was closed after an Indian died in police firing. Nepalese authorities clamped a curfew in Birgunj following the violence.
Similarly, crossings to and from Jogbani-Biratnagar border post have been halted by Indian security forces.
Two other border points in western Nepal, at Rupaidiya-Nepalgunj and at Sunauli-Bhairahawa, are also blocked.
PN Singh, the local commander of the 7th Sashastra Seema Bal (SSB) Battalion, told the media that the border points will be sealed for two days.
The SSB has been allowing only pedestrians to cross the border. Some vehicles bearing Nepal number plates entered through the Rupaidiya customs point on Monday. So did some fuel tankers and trucks.
The decision to shut down the entry points was not communicated to the Nepalese authorities, said Nepal's officials.
The India-Nepal border has been tense after Madhesh-based political parties in the Himalayan nation held massive protests against Nepal's new constitution.
In the process, movement of fuel and other essential items from India to Nepal have been badly hit, causing widespread shortages in that country.