Video footage obtained by the Enquirer shows the jib broke free and fell on to the site.
Ballymore confirmed that no-one was injured in the incident at the Royal Wharf site.
The developer said the Spierings mobile self-erecting tower crane was owned and operated by City Lifting.
A spokesperson from Ballymore said: “There was an incident on site at Royal Wharf with a crane on Wednesday morning.
“An investigation is underway. We can confirm no one was injured.”