The move follows the injury to Australia's Shaun Marsh who is currently out with a broken arm suffered in the nets.
His brother, all-rounder Mitch Marsh, is currently due to join the county after the first four games.
Fakhar has played 30 T20 matches for Pakistan.
The 29 year-old left-hander has been a regular for Pakistan in the World Cup with a top score of 62 against India, taking his tally to 44 appearances in the international 50-overs format, BBC Sports reported.
Glamorgan begin their Blast campaign at home to Somerset on Thursday 18 July.
Their current overseas player, Australia's Marnus Labuschagne, is due to leave at the end of the current Championship match against Middlesex because of Australian squad commitments.