NAJAF, Iraq (Reuters) - Iraq's first coronavirus case, an Iranian theology student, has been detected in the holy city of Najaf, the health ministry said on Monday, leading authorities to briefly close the gates to one of holiest sites for Shi'ite Muslims.

The patient entered Iraq before the government shut border crossings and banned the entry of non-Iraqis coming from Iran.

"The results of lab tests conducted on a theology student, an Iranian citizen, who had entered the country before ... the decision to stop travel have revealed he is ill with the coronavirus," a ministry statement said.

The patient is in quarantine and medical staff are observing international health standards, the statement added.

A local health source said all students in the religious school attended by the patient were being quarantined and tested for the virus. Najaf's education authority ordered mid-year exams to be postponed.

The gates of the Imam Ali shrine and mosque, which house the remains of the Prophet Muhammad's cousin Ali - a central figure in Shi'ite Islam, were closed off and the area was disinfected before they were reopened. The site receives thousands of pilgrims daily and at least 8 million a year.

Fears of a coronavirus pandemic grew on Monday after sharp rises in new cases in Iran, Italy and South Korea. The virus has infected nearly 77,000 people and killed more than 2,500 in China, where it originated late last year.

Iraq had earlier on Monday shut its Safwan border crossing with Kuwait to travelers and trade at Kuwait's request, the local mayor told Reuters.

Kuwait and Bahrain recorded their first coronavirus cases, all people who had visited Iran, state media said.

Iraq on Saturday extended for 15 days an entry ban for non-Iraqis coming from Iran, which has confirmed 61 cases and 12 deaths.

Neighboring Iraq and Iran, both home to Shi'ite Muslim majorities, share close religious, political and trade ties.

(Reporting by Reuters correspondent in Najaf; Writing by Ahmed Aboulenein; Editing by Giles Elgood and Ed Osmond)