Try this,
Use ClipRRect and nest inside another Container and now you can add non-uniform borders
Container(
decoration: BoxDecoration(
color: Colors.white,
borderRadius: BorderRadius.circular(10),
boxShadow: [BoxShadow(color: Colors.black12, blurRadius: 5)],
),
child: ClipRRect(
borderRadius: BorderRadius.circular(10),
child: Container(
padding: EdgeInsets.all(20),
decoration: BoxDecoration(
border: Border(
left: BorderSide(color: Colors.indigo, width: 5),
),
),
child: Column(
mainAxisSize: MainAxisSize.min,
children: <Widget>[
Icon(Icons.home),
Text("Home"),
],
),
),
),
)