I found the great success of Slack was reducing interruptions. It replaces things that would have otherwise been a "hard" interruption (in-person conversation or phone call) with a "softer" interruption (notification). And it provides a much better way for people who need to speak with "someone from the x team" to talk to whoever happens to be relatively free at the moment, rather than picking someone to interrupt.

(Also are you sure minimizing interruptions should be a goal? If you cut off all communications you'll avoid interruptions, but that probably won't be good for your business)