Officers were called at just before 8pm to reports of man attempting to climb the bridge structure.
MOD, Fire, Police and Ambulance all attended the scene, and the bridge was closed whilst the incident took place.
A Devon and Cornwall Police spokesperson said: "Just after 8:30pm the man climbed down following discussions with police and was safely taken into custody; the bridge was fully reopened before 9pm.
"A 29-year-old man from Saltash remains in police custody on suspicion of causing a public nuisance and resisting arrest."