Opening batsman Eddie Byrom and opening bowler Timm van der Gugten will both miss Glamorgan's match against Middlesex at Lord's on Friday, April 5.
Byrom dislocated his shoulder during training, while van der Gugten is suffering from a calf injury.
Byrom has had a string of fitness setbacks, including a freak hip injury in 2023 and an infection in 2022.
Former Northants player Toby Bailey has joined the coaching staff on a short-term basis. He will then rejoin Scotland for the T20 World Cup in June.
Bailey, 47, previously worked with new head coach Grant Bradburn in Scotland.
Mark Walton, one of Matthew Maynard's assistants, has left to take up a scouting role for West Ham United.
Walton used to play in goal and had spells with Cardiff City, Brighton and Hove Albion, and Fulham.
The annual general meeting of members in Glamorgan also confirmed the appointment of former player Alan Wilkins as president. Wilkins later became a sports presenter for BBC Wales.