Is this common practice?
I do not think so. I have worked in US as well as Indian companies and never heard of manager making that request. Every place I worked (and resigned), I was free to let people know about my plans whenever I am comfortable. My last manager asked me to wait until an official announcement is made to my team which was within short period of resignation. (He was also hoping that he could change my mind in the meantime!)
If so, what are some reason(s) behind this request?
I think it is counter productive not to tell in advance because others will plan something assuming your presence. So while disruption of work could be one reason as other have pointed, I think it will serve the purpose in exactly opposite way.
I think this largely is coming from insecurity of the company. They may be afraid that during your notice period, you will get a chance to talk about reasons for your leaving and others will identify themselves with those reasons and get ideas!! Or you will 'expose' a big flaw in the company which made you unhappy and then (mis)lead others on the same path.
I do not think a healthy and professional working atmosphere will allow this.