I needed to do the same thing, But there is nothing relevant functionality I found in the MapBox sdk. So, I figure out something on my own. I customized MapView of MapBox sdk with enabling/disabling pan feature. For that I used SimpleTwoFingerDoubleTapDetector . Thanks @Sam for this above class which helps me to detect two finger double tap.
My custom MapView class:
MyMapView.java:
import android.content.Context;
import android.os.Handler;
import android.support.v4.view.GestureDetectorCompat;
import android.util.AttributeSet;
import android.view.GestureDetector.OnDoubleTapListener;
import android.view.GestureDetector.OnGestureListener;
import android.view.MotionEvent;
import android.widget.Toast;
import com.mapbox.mapboxsdk.tileprovider.MapTileLayerBase;
import com.mapbox.mapboxsdk.views.MapView;
public class MyMapView extends MapView implements OnGestureListener,OnDoubleTapListener {
    private GestureDetectorCompat mDetector;
    public boolean panShouldEnabled = true;
    public boolean isPanShouldEnabled() {
        return panShouldEnabled;
    }
    public void setPanShouldEnabled(boolean panShouldEnabled) {
        this.panShouldEnabled = panShouldEnabled;
    }
    public MyMapView(Context aContext, AttributeSet attrs) {
        super(aContext, attrs);
        init(aContext);
    }
    private void init(Context mContext) {
        mDetector = new GestureDetectorCompat(mContext, this);
        // Set the gesture detector as the double tap
        // listener.
        mDetector.setOnDoubleTapListener(this);
    }
    public MyMapView(Context aContext, int tileSizePixels,
            MapTileLayerBase tileProvider, Handler tileRequestCompleteHandler,
            AttributeSet attrs) {
        super(aContext, tileSizePixels, tileProvider,
                tileRequestCompleteHandler, attrs);
        init(aContext);
    }
    public MyMapView(Context aContext, int tileSizePixels,
            MapTileLayerBase aTileProvider) {
        super(aContext, tileSizePixels, aTileProvider);
        init(aContext);
    }
    public MyMapView(Context aContext) {
        super(aContext);
        init(aContext);
    }
    @Override
    public boolean onInterceptTouchEvent(MotionEvent ev) {
        return !panShouldEnabled ? true : super.onInterceptTouchEvent(ev);
    }
    @Override
    public boolean onTouchEvent(MotionEvent event) {
        // TODO Auto-generated method stub
        if (!panShouldEnabled) {
            if (detector.onTouchEvent(event)) {
                return true;
            } else {
                mDetector.onTouchEvent(event);
            }
        }
        return !panShouldEnabled ? true : super.onTouchEvent(event);
    }
    @Override
    public boolean onDown(MotionEvent arg0) {
        // TODO Auto-generated method stub
        return false;
    }
    @Override
    public boolean onFling(MotionEvent arg0, MotionEvent arg1, float arg2,float arg3) {
        // TODO Auto-generated method stub
        return false;
    }
    @Override
    public void onLongPress(MotionEvent arg0) {
        // TODO Auto-generated method stub
    }
    @Override
    public boolean onScroll(MotionEvent arg0, MotionEvent arg1, float arg2,
            float arg3) {
        // TODO Auto-generated method stub
        return false;
    }
    @Override
    public void onShowPress(MotionEvent arg0) {
        // TODO Auto-generated method stub
    }
    @Override
    public boolean onSingleTapUp(MotionEvent arg0) {
        // TODO Auto-generated method stub
        return false;
    }
    @Override
    public boolean onDoubleTap(MotionEvent event) {
        zoomIn();
        return true;
    }
    @Override
    public boolean onDoubleTapEvent(MotionEvent event) {
        return false;
    }
    @Override
    public boolean onSingleTapConfirmed(MotionEvent arg0) {
        return false;
    }
    SimpleTwoFingerDoubleTapDetector detector = new SimpleTwoFingerDoubleTapDetector() {
        @Override
        public void onTwoFingerDoubleTap() {
            Toast.makeText(getContext(), "Two Finger Double Tap", Toast.LENGTH_SHORT).show();
            zoomOut();
        }
    };
}
So, now when you'll access your mapview in your Activity :
mapView = (MyMapView) findViewById(R.id.mapid);
//Here you can play with enabling/disabling pan. 
mapView.setPanShouldEnabled(false);
It might help someone. :)