A 37-year-old man was critically injured after he plunged from the balcony of an inner Sydney apartment on Sunday, sparking a police search for a man he had met up with via a dating app earlier that day.

Detectives are searching for the other man who they say is a potential witness to the "life-threatening" fall at the Surry Hills unit block after they met up using Grindr.

The injured man, who is an American and Swedish national, is believed to have fallen four floors onto a ground-floor patio, impaling himself on a table leg shortly before 4pm Sunday.

Police said the man was seen climbing over the balcony railing of his own volition before he fell.