The Fringe act Dolls, who work with the Cirk La Putyka, carried out the stunt above traffic on Friday.
Josa Koelbel and Bellina Sorensson, from the Czech Republic, dangled from the bridge in a bid to promote their show at the Underbelly Lafayette tent.
Edinburgh City Council said the performers had failed to apply for a licence.
An Edinburgh city council spokeswoman said: "The council was not made aware of this performance which was not permitted or authorised."
A Police Scotland spokesman said: "Any artistic performance, event or demonstration where public safety considerations are required must obtain an appropriate licence from the City of Edinburgh Council.
"Failure to obtain the necessary licence may result in a joint inquiry by the police and council licensing board into the matter."
The circus was not available for comment.
A police investigation has been launched into a Fringe trapeze stunt from an Edinburgh city centre bridge.