The incident happened at about 4pm on Sunday on Ingham Road, in the Thornhill Lees area of the town.
The girl was with her 16-year-old sister when a man approached them and “took hold” of her.
He also assaulted the 16-year-old before letting the younger girl go and making off in the direction of Parker Road.
Kirklees CID’s Det Insp Mark Catney said: “We are continuing to carry out extensive enquiries and are keen to trace the man pictured in the e-fit as he may have information valuable to the investigation.
“The two girls involved were obviously shaken by what happened and their family is being supported by officers.
“We appreciate this incident may have caused concern amongst the local community and we will continue to have an increased police presence and patrols in the area to offer reassurance.”
Anyone with information is asked to ring West Yorkshire Police on 101.