The Star Trek: The Next Generation Technical Manual (considered, if not entirely canon, at least a quasi-official authoritative source), gives the following description of the Captain's Yacht:
The yacht is capable of sustained sublight velocities
approaching 0.65c. The impulse propulsion system (IPS)
consists of six sequential beam-fusion reaction chambers
feeding a central toroidal driver coil. Each chamber measures
1.3 m in diameter and is similar to its larger IPS cousins on the
Enterprise. The reaction exhaust is vented through the driver
coil and magnetohydrodynamic (MHD) accelerator for impulse travel. The MHD tap provides power to the navigational
deflector grid for removal of interstellar dust and gas from the
vehicle flight path. For atmosphere flight the exhaust is
redirected after it exits the MHD tunnel and sent through the
aerodyne engines around the ellipse equator. The normal
atmosphere cruising velocity is Mach 6; maximum safe waverider velocity is Mach 20. Magnetic turbulence contour equalizers, variants of the navigational deflector, provide momentum conditioning at Mach transitions.
The Enterprise is designed to operate safely without the
yacht in place, since its structural integrity field and inertial
damping fields produce slightly modified fields in those areas
to compensate for the concavity of the yacht docking structure. Yacht operational rules in the vicinity of the starship are
generally the same as those for other auxiliary spacecraft,
with the difference being that the yacht, during emergency undockings, may be safely deployed at velocities as high as
Warp Factor 7. The yacht's systems are designed to afford the
craft a smooth falloff of warp field, though the decaying field
energy cannot be sustained for any appreciable time.
It explicitly states that the Yacht is equipped with an Impulse Engine, but doesn't provide any information about a Warp Propulsion System, seemingly implying that it has none; also, the statement that it can be detached from the starship traveling at Warp speed and perform a "smooth falloff of warp field" seem to further imply that it can't sustain warp speeds on its own.
On the schematic that is present on the Manual, some systems are detailed (including the Impulse engine), but also here there is no mention of a Warp engine: