Решил вопрос след. образом:
App.js<Router history={this.props.history}>
<Switch>
<Route exact path="/" name="Home" component={Index} />
<Route path="/colors" component={Palette} />
<Route path="/icons" component={Icons} />
<Route path="/forms" component={Forms} />
<Route path="/other" component={Other} />
<Route strict path="/dashboard" component={Dashboard} />
</Switch>
</Router>
Dashboard.jsrender() {
return (
<div className="DashboardComponent">
// ...
<Switch>
<Route exact path="/dashboard/my-account" component={MyAccount} />
<Route exact path="/dashboard/service-request" component={ServiceRequest} />
<Route exact path="/dashboard/payments" component={Payments} />
<Route exact path="/dashboard/settings" component={Settings} />
<Redirect to="/dashboard/my-account" />
</Switch>
</div>
)
}