Looks like we have one, name “National Information Technology Center” and that runs/provides services to government offices only inside Singha Durbar.
From Ministry of science, technology and environment
http://moste.gov.np/%E0%A4%B8%E0%A4%82%E0%A4%B8%E0%A5%8D%E0%A4%A5%E0%A4%BE%E0%A4%B9%E0%A4%B0%E0%A5%81/nitc
The National Information Technology Center (NITC), situated in singha durbar, Kathmandu was established in the year 2002 in line with IT policy 2000 under Ministry of Science and Technology with the vision of developing and promoting Information Technology Sector of Nepal. Currently it is working as government’s central ISP. It also manages singha durbar e-gate pass system and optical fibre connection within different ministries and departments inside singha durbar area. It also focuses on Telecenter establishment and basic and advance IT trainings for government employees. It has also started E-government implementation for creating transparent interaction between government and citizens(G2C), government and business organizations(G2B) and different government organizations(G2G) in Nepal.