Old English scapan, past participle of scieppan "to create, form, destine" (past tense scop), from Proto-Germanic *skapjanan "create, ordain" (cf. Old Norse skapa, Danish skabe, Old Saxon scapan, Old Frisian skeppa, Middle Dutch schappen "do, treat," Old High German scaffan, German schaffen "shape, create, produce"), from PIE root *(s)kep- a base forming words meaning "to cut, scrape, hack" (see scabies), which acquired broad technical senses and in Germanic a specific sense of "to create."
Old English scieppan survived into Middle English as shippen, but shape emerged as a regular verb (with past tense shaped) by 1500s. The old past participle form shapen survives in misshapen. Middle English shepster (late 14c.) "dressmaker, female cutter-out," is literally "shape-ster," from Old English scieppan.
Meaning "to form in the mind" is from late 14c. Phrase Shape up (v.) is literally "to give form to by stiff or solid material;" attested from 1865 as "progress;" from 1938 as "reform;" shape up or ship out is attested from 1956, originally U.S. military slang, with the sense being "do right or get shipped up to active duty."