A torque rod apparatus for a vehicle may include a damper supported at an outer circumference thereof by a lower frame of the vehicle, with a first hollow portion being axially formed in the damper, an inner core inserted into the first hollow portion of the damper, with a second hollow portion being axially formed in the inner core, an insert opening formed partially through the damper and the inner core in a radial direction to allow an interior of the inner core and an exterior of the damper to be bored through, and a linkage connected at a first end thereof to a drive unit, with a through hole formed in a second end thereof, the second end being inserted into the insert opening to allow the linkage to be integrally coupled to the lower frame of the vehicle and the inner core.