Libby Squire was last seen by her friends getting into a taxi outside The Welly on Beverley Road, Hull, at about 23:00 on Thursday.
The University of Hull student was then seen by a man who tried to help her at 23:45 near Beresford Avenue.
Det Supt Simon Gawthorpe said her disappearance was out of character.
Speaking at a press conference, he said: “Her family have described Libby as a very thoughtful young woman who always put other people before herself.
“They have said this is very out of character for Libby, and clearly that raises our concerns about her significantly.”