You need to run away with [ , otherwise it will start its work in the group and select in / in your data.
sed -n '/^\[2015\/01\/01 03:46/,/^\[2015\/01\/01 03:47/p' Input.txt
or (thanks to nu11p01n73R)
sed -n '\|^\[2015/01/01 03:46|,\|^\[2015/01/01 03:47|p' Input.txt
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