Oli, 70, had been feeling uneasy, and a polymerase chain reaction test conducted on Saturday had returned positive.
Both India and Nepal claim Kalapani as an integral part of their territory -- India as part of Uttarakhand's Pithoragarh district and Nepal as part of Dharchula district.
Nepal shares a border of over 1,850 kms in the east, south and west with five Indian states, Sikkim, West Bengal, Bihar, Uttar Pradesh and Uttarakhand.
The prime ministers of the two countries will jointly inaugurate the Janakpur-Ayodhya direct bus service, which will put Janakpur on the Ramayana tourist circuit.
Modi said the two countries have completed several bilateral connectivity and development projects in the last few years.
The pilgrimage refers to Modi’s planned visit to Janakpur—where he will offer prayers at the Janaki temple before going to Kathmandu for official engagements—and Muktinath.
Nepal's prime minister is also expected to push for India to complete previously promised infrastructure projects, many of which have limped along for decades.
Oli, 65, served as the country's prime minister from October 11, 2015 to August 3, 2016. He is known for his pro-China stance.