Rabbits do climb (Google Rabbits Climbing) and jump to high places. Ours have a 5 foot tall condo in the living room, which they would make their way top of we had a very difficult time arranging things so they could not get there.
Rabbits will jump from heights that can injury them. Rabbits can and do injure themselves from falls & jumping down from as little as four feet. At the same time unless they are motivated to leave they will stay in 2 (.6m) foot pen. When we are outside (supervised) we use a 2 foot (.6m) pen to define the boundary for the same rabbits that go to the top of 5 foot (1.5m) condo. Johns idea of floor to ceiling coverage is very good, though I would use plastic lattice as it holds up better and is more attractive (and more expensive).
If the balcony has a roof and you are ALWAYS going to be on the balcony with the bunny any kind of coverage that is to small for them to fit through and is 2 foot high would be the minimum required.
We foster rabbits for short periods of time (a couple weeks to a couple of months) that are proven climbers and jumpers of 4 foot enclosures. We find that a 3 foot (.9m) high wall that they can not see through, or over, keeps them in; they tend not to climb or jump over things if they can't see what is on the other side.
So if your rabbit is going to occasionally be on a covered balcony, and you will be away for SHORT periods of time, a 3 foot no see through enclosure would be the minimum required.
If the rabbit is going to be on the balcony for more then a few minutes without supervision, complete bunny proof coverage from floor with a ceiling is required.