There is certainly a collection of apps you can use for this. One of the keywords to check is Geo-Fencing here, available with a bunch of e.g. "child protection" apps (see: Location Monitoring): you define the area your "child" (here: car) is permitted to be in, and as soon as it leaves that area (your car moves) an alert is triggered. Examples here are GPS or Network Tracking (not too many permissions requested; alerts per SMS) or tinyTraker.
Alternatively, whenever something shall be automated, I always think of Tasker – which of course also can deal with GeoFences, and can send alerts in many ways – e.g. per SMS or mail. Tasker doesn't come entirely for free (though there's a 7-day trial available on its website), but it can do a lot of things, so you might at least wish to check. For that, I recommend taking a look at my collection of Tasker resources.
I must admit I have no experiences in this area (Geofencing), so I cannot tell you how well the mentioned Android apps work. But the first two are free, so you can at least try them out – and Tasker is known to be "the non-plus-ultra automation app on Android".