Tymal Mills, the Sussex left-arm seamer, will miss the rest of the Vitality Blast with a back injury.
A club statement said that Mills had been experiencing discomfort during the tournament, and that further investigation revealed that was due to a lumbar spinal injury that required a period of rest. Mills has starred for Sussex with the ball this season, taking seven wickets and giving up just 6.52 runs per over.
His career has regularly been set back due to injury, but the club clarified that the injury is separate to the thoracic spine condition that led to Mills' decision to become a T20 specialist in 2015.
With Rashid now departed ahead of Afghanistan's tri-series against Bangladesh and Zimbabwe, it means that Sussex are without two key bowlers for the rest of the competition, while Jofra Archer is highly likely to miss the majority due to Ashes commitments.
As a result, they have moved quickly to sign Behrendorff, who is expected to link up with the squad after the ongoing Championship fixture against Middlesex.
Meanwhile, Surrey have lost Tom Curran for the rest of the season, after he pulled up with a side strain during the final over of Thursday's win against Sussex at The Oval. Curran will undergo rehabilitation work with the Surrey and England medical teams, and hopes to be fit in time for the five-match T20I series against New Zealand in November.