The video shows two masked men firing a volley of shots over the coffin of veteran republican Victor Notarantonio, who died last week. The display was followed by a round of applause.
Ms Eastwood said the display was concerning.
“I am deeply disgusted by this footage – there is no place whatsoever for gunmen in our society. Police must fully investigate this incident, as there can be no acceptance of any type of paramilitary displays.
“If anybody has any information about this display, I would urge them to contact the police immediately.”