Navagio is one of the island's main attractions, with the beach featuring a shipwreck on the shore.
The video, posted on the island's official Twitter account, shows a large chunk of the cliff face falling as tourists below scatter. The videographers no doubt ran when they realised what was happening.
The coast guard said one foreign woman was injured and was being transported to a local hospital. She was hospitalised together with her husband and two children, who suffered minor injuries.
As reported by the Evening Standard, Josh O'Connell, 21, of Kilkenny, Ireland works for a local tour company and described the terrifying scene.
"There was a rumble and a rock fell, followed by a larger rock and then another". (Supplied) Small boats at the beach were capsized as a result of the fall sparking big waves.
He said: "I thought more was coming and I just started running".
The water hit his feet with such a strong force, it knocked him onto his back and went on to cover more than half the beach.
The rock's weight drove waves on to the crowded beach, Mr O'Connell said, as families scrambled to safety.
"So far, we haven't found any trapped people but we will continue searching", a fire brigade official said. Rescue services employed sniffer dogs to search the beach itself for possible victims of the rockfall.
Tourists board a boat at the beach Navagio following a rockfall, on the island of Zakynthos, Greece September 13, 2018.
Lynette Bridges, 58, was on a tour boat, pulling up to "Shipwreck Beach" as the incident happened.
British woman Wendy Thorpe said she was on a boat with her daughter when the cliff collapsed and there was an "almighty crash".