The 20-year-old USA youth international has recently returned to playing following his recovery from a serious leg injury
. Packwood, who can play in either the centre of defence or as a full-back, suffered a double leg fracture in Blues' FA Cup third round tie against Leeds United in January.
Blues boss Lee Clark sees the move as the ideal way for the American to get much-needed match action under his belt.
To date, this season he has made four league appearances for Richard Beale's development squad
but has yet to figure for the first-team.
Bristol Rovers, who are managed by John Ward, are currently 20th in the table, two points above the drop zone.
Packwood's loan spell runs up to and including Saturday 16 November but has not been given permission to play in the FA Cup.
The Blues Academy graduate will be eligible to play in the Pirates' home fixture against Wycombe Wanderers this coming Saturday.