While there does not seem an out of the box way to achieve this, but you can achieve this using a custom lightning component not really to embed the dashboard in the component itself but an approach to navigate to the dashboard.
For navigating to the dashboard, what you can do here is to utilize force:navigateToURL
event to navigate to a particular dashboard. The custom lightning component will display all applicable dashboards say in a select option, where you map their respective ids. And upon selecting the respective dashboard, you just have the event navigate to it. It just depends on how you want the UX to be displayed, but ultimately using force:navigateToURL
can be utilized to achieve the use case.
As an example, this is how your component and JS controller will look like.
Component
<aura:component>
<lightning:select aura:id="selectItem" label="Select a Dashboard" onchange="{!c.navigateToDashboard}">
<option value="">Choose a Dashboard ...</option>
<option value="idofdashboard1">My Dashboard 1</option>
<option value="idofdashboard2">My Dashboard 2</option>
</lightning:select>
</aura:component>
JS Controller
navigateToDashboard : function(component, event, helper) {
var dashboardId = component.find("selectItem").get("v.value");
var urlEvent = $A.get("e.force:navigateToURL");
urlEvent.setParams({ "url": "/" + dashboardId});
urlEvent.fire();
}