The UN mission in Juba said staff there were under lockdown and that the shooting was continuous.
Correspondents say the firing appeared to be focused around military barracks in the city.
Army spokesman Phillip Aguer told residents to "remain in their residences until we establish the actual cause of the shootings".
South Sudan broke away from Sudan after a referendum in 2011 and decades of conflict. Numerous armed groups remain active in the oil-rich country.
Tensions have been high since President Salva Kiir dismissed his deputy Riek Machar in July in an apparent power struggle.
A Reuters reporter in Juba said the fighting had gone on through the night but intensified in the early morning.
The army spokesman said the military regretted the situation but gave no details of casualties, the Sudan Tribune reports.
The UK and US embassies in Juba also urged their citizens via Twitter to stay indoors and exercise caution.
The US statement to citizens said the embassy had "received reports from multiple reliable sources of ongoing security incidents and sporadic gunfire in multiple locations across Juba".
- BBC
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