Local police chief Keshav Adhikari confirmed that Paras Shah had been detained and was being questioned about the incident.
Mr Shah, the only son of deposed King Gyanendra, admitted firing his gun but defended his action, saying that he could not bear to hear insults against his family and country.
He said in a statement that two guests at a restaurant at a resort in southern Nepal had made "baseless and provocative remarks against his role and the institution he represented".
Mr Shah said that he left the restaurant, returned half an hour later and fired his gun into the air once, without harming anyone or causing damage.
He then fled to another resort in Pokhara, 125 miles west of Katmandu, where he was detained.
Local television stations reported that police officers had taken complete control of the resort.
During his years as crown prince, Mr Shah was often criticised for hard partying and frequent brawling.
Several street protests were held against him, but he has never faced a criminal investigation or charges.
Nepal's Constituent Assembly abolished the centuries-old monarchy in 2008.
Mr Shah moved to Singapore with his wife and children after the abolition, but remains a frequent visitor to Nepal.
King Gyanendra assumed the throne in June 2001 after his elder brother, King Birendra, was killed - along with his family - in a massacre inside the royal palace.
A government investigation was ordered into the massacre, in which ten people died, but the report was inconclusive and left some questions unanswered. Many Nepalis suspect Gyanendra and Mr Shah were somehow involved in the slayings.
Gyanendra seized absolute power in 2005, but pro-democracy protests in 2006 forced him to give up his authoritarian rule and restore democracy.
Two years later, the monarchy was abolished and Nepal was declared a republic.REFUGEE RESETTLEMENT
A CAMPAIGN to resettle ethnic Nepalese forced out of Bhutan two decades ago has found homes for 40,000 refugees in Western countries, but tens of thousands are still waiting, officials have said.
More than 100,000 ethnic Nepalese - a Hindu minority in Bhutan for centuries - were forced out in the early 1990s by authorities who wanted to impose the country's dominant Buddhist culture. They have lived as refugees in Nepal ever since. The United Nations - with the help of the United States and other countries - set up the resettlement programme in July 2007. More than 60,000 refugees originally signed up.
The first refugees began leaving Nepal in November 2007 and they have resettled in countries including the US, Britain, Canada, Australia, New Zealand, Norway, Denmark and the Netherlands.