Officers became suspicious after smelling the drug and searched the man in the early hours of Saturday morning.
They found a lock knife in his pocket.
The man was taken to custody.
Sergeant Jordan McGowan shared the discovery on Twitter.
The officer said: "Out patrolling Leeds City Centre and caught a whiff of cannabis which on searching the person I found this lock knife in his pocket.
"He’s now spending the night in custody suite at Elland Road Police Station."