Of the two new patients, one is a 65-year-old woman from Kailali and the other is a 19-year-old boy in Rautahat.
This takes the nation-wide tally to 14 with one recovery and zero deaths so far.
Nepal has been under a complete lockdown since March 24 to curb the spread of deadly virus.
Monday also marks the first day of the Nepalese New Year 2077 when people perform various rituals and welcome the New Year.
All these celebrations have been cancelled in the wake of the coronavirus crisis. People have been asked to mark the occasion in their homes only.
Nepalese Prime Minister KP Sharma Oli in a nation-wide address said, "At this time we should have been welcoming New Year with fervor and happiness bidding farewell to the bygone year, learning lessons from it and making resolutions but we are now welcoming this year in an unpleasant situation."
The Prime Minister said that the situation would be assessed again on April 15 and steps that have to be taken thereafter to control the spread of the virus would be taken.
( With inputs from ANI )