Nepal Airlines and several Indian carriers cancelled flights on Tuesday.
It affects services from Delhi on Air India, IndiGo and SpiceJet.
Air India and Spicejet said Wednesday’s Kathmandu flights are currently suspended, while IndiGo hopes to resume service later today.
One airline source told Indian media that an Air India flight turned around when it was already on its approach into Kathmandu after seeing smoke coming from the airport building.
A later Air India flight was diverted to Lucknow.
“In view of the current situation in Kathmandu, the Delhi-Kathmandu-Delhi route have been cancelled. We are closely monitoring the situation and will share further updates,” Air India said
The flag carrier operates six flights a day to Kathmandu.
India has advised citizens not to travel to Nepal.