The crash happened on the A4232 Ely link road between junction 33 of the M4 and Culverhouse Cross on Friday.
A tweet from South Wales Police's roads policing unit said: "Person/s made off but left behind large amount of drugs.. Please call 101 if you wish to claim them. (Inc 56) #Team4East".
Police said later that a man was in custody for drug and road offences.
Police have sent a tongue-in-cheek invitation to the owner of a stash of drugs found after a Cardiff car crash.