Bangor Protestant Boys Flute Band were marching in Agincourt Avenue in the Holyland area of south Belfast as part of the Twelfth demonstration when the morning incident occurred.
One man has been arrested and items, including a black wheelie bin, were taken away by the PSNI for examination.
A man was captured on mobile phone footage leaving the property and throwing an object in the direction of the bandsmen, who were parading in formation down the street. An Irish tricolour could be seen flying from an upstairs window in the property.
Members of the band could be seen standing and looking at the object. One appeared to take a photo of it on their phone.
The window of a downstairs property, belonging to an elderly resident completely unconnected to the incident, was smashed after a wheelie bin was hurled at the property by a man wearing a band uniform.
The entire incident, barely a minute in length, was captured on a mobile phone and posted online. It has since been viewed thousands of times.
Bangor Protestant Boys, represented by loyalist Jamie Bryson, released a statement saying: “In the split second following this unprovoked and entirely unexpected sectarian attack, there were genuine and legitimate concerns amongst band members that an explosive device had been thrown into the ranks.
“In this context, the band showed remarkable restraint and thankfully calm was quickly restored to the situation. In the confusion following the attack on the band, regrettably an item smashed the window of the general property from which the aggressor came.
“Unbeknown to the band members, the property is split into different homes over several floors and regrettably the window smashed did not in fact belong to the aggressor, but rather an entirely innocent victim of this situation, who had been endangered by the aggressive sectarian attack launched by their neighbour.
“The band will pay for all damage to the innocent person’s window and express apologies to this individual.”
A PSNI officer on the scene and other members of the band then appear to usher those involved away from the property.
The PSNI said: “We are aware of footage circulating online involving a number of parties in the Agincourt Avenue area of south Belfast.
“We have arrested a 46-year-old man on suspicion of a range of offences including assault and disorderly behaviour.
“Detectives are currently investigating other potential offences and persons.”
Images on social media also later showed the PSNI recovering the bin used in the incident.