What is the most professional way to handle the situation?

Immediately forward the call to voicemail. The best thing to do in this situation is immediately forward the call to voicemail. Unless you are waiting for an important work-related call, most calls can wait until you are done with the customer.

Just letting the phone continue ringing is distracting. quickly answering the phone saying, I am busy right now, I willcall you right back is sometimes appropriate, but it distracts from the conversation with your customer and should be avoided if possible.