CRJ-900 Captain reported ground crew disconnected the tow before the crew set the parking brake causing the aircraft to momentarily move forward before the crew applied the brakes.

Narrative

We were pushing back from the gate in ZZZ. Motion had stopped and I was waiting for the tug driver to say 'set brake.' All of a sudden the aircraft began to roll forward and at the same time the tug driver said 'brakes!' over the Intercommunication Systems in a loud and urgent tone; and both me and my FO stepped on the brake pedals; and the aircraft stopped rolling. The tug driver then informed us that the nose gear tire had rolled forward on top of the 'horseshoe'. He asked me what I wanted to do. I asked him; can I set my parking brake now and he said yes; so I set the parking brake. I then said I wanted maintenance to come out and look at the situation before I decided what to do. Maintenance did come out and looked at it; and we decided to let the crew pull the horseshoe out from under the tire; then maintenance would inspect the nose gear and determine if we were safe to continue taxi and flight. They did then pull it out; the inspection was completed; I wrote it up; and maintenance cleared the write up and we then continued the flight uneventfully. The cause of this incident is that the ground crew disconnected the tow bar prior to asking me to set the parking brake.