The NHTSA has received seven complaints, including four injury reports.
The agency has identified at least seven complaints alleging unintended movement after the driver switched the transmission gear selector to Park with the engine running and after the driver exited the vehicle.
"Four complaints reported the vehicle moving while the driver door is open resulting in injuries requiring medical attention and one complaint reported being pinned against a garage wall," the NHTSA notes.
Like the Ram and Dodge vehicles that prompted a similar rollaway investigation, the Evoque and XF use a rotary knob to switch the transmission gear.
In an earlier Fiat Chrysler Automobiles rollaway investigation, the company was pressured to recall around a million vehicles equipped with shifters that apparently caused confusion among buyers.