Are you trying to open shapefile data or adding other (non shapefile) data?
If a shapefile, sounds like you are trying to move one of the component files of a shapefile . A "shapefile" actually consists of several separate files (as seen in Windows Explorer). Basic shapefile will have four files - .shp, .shx, .dbf, .cpg - with potentially others (e.g. a .prj file if the files has a coordinate system described for it). All the files must be in the same folder location and cannot be separated.
If you are trying to add other data (e.g. .dbf file of point data which has coordinates) try adding through File > Add Data > Add XY Data - you can select the data location and match the XY coordinates to the relevant dbf file field names.