YES! A Nepali citizen can be employed in India, as well as an Indian citizen in Nepal. You have to ensure that the documents are proper and legal for both parties.
Employment Agreement Between India and Nepal
According to the pact signed by both countries (India and Nepal) in 1950, they are also applicable to regular employee benefits. Even the Indian government has been employing Gurkhas (citizens of Nepal) in Defense (all three wings), and they are also eligible for most UPSC examinations. The eligibility sections contain "Indian citizen or a subject of Nepal" when viewed in Employment News or online while appearing for the examination.
Visa and Work Permit Requirements
Any kind of VISAs or work permits are not mandatory between the two countries, just proper legal documents are required for verification and identification of the individuals as in the case of Indian citizens. Many Indian citizens work in the border areas of Nepal in various industries like garments, retail, education, etc. These two countries share an open border in which both parties are allowed to stay and work.
I hope this information helps.
Regards,
Madan S.T.