The shower head has been leaking & I have removed the head but water is still dripping from the arm. How can I fix it?

Which end of the arm is dripping, where is connects to the head or where it screws into the wall, aka drop ear as its called in the trades.

Shower are is leaking because your faucet keep refilling it. You will need to replace washers or cartridge in your faucet to stop the leak. Milo

Milo hit it! What type of shower valve do you have? One handle or two knobs? What's the brand name? How old? Back to you, Tom

Milo is likely correct. I read this as a leak when the shower was in use. However if the "arm" leak, that threw me, when the shower is not being used then a leaking valve is the issue. Hard to tell when the OP doesn't come back to answer questions or fully explain the issue.