In a brief statement released on Tuesday, the Royal Oman Police said that the incident took place in the vicinity of a mosque in Muscat’s al-Wadi al-Kabir neighborhood.
Officers responded to the incident, the police added, giving an initial toll of four killed and "several others" injured.
Footage on social media shows people fleeing near Imam Ali Mosque as gunshots ring out.
The shooting occurred as Shia Muslims are marking Ashura to commemorate the martyrdom anniversary of Imam Hussein (PBUH), the third Shia Imam and the grandson of Prophet Mohammad (PBUH).
"All security measures and procedures have been taken to deal with the situation, and procedures for gathering evidence and investigation are being completed," read the police statement.
Following the shooting, the US Embassy in Muscat issued a security alert and canceled all visa appointments on Tuesday.
Such an attack is rare in Oman, which regularly plays mediating roles in regional conflicts.
Press TV