Daley's 3m mixed synchro partner Grace Reid will also miss the event in her home city held between 1-4 June.
The British Championships double as qualifiers for July's World Championships in Hungary.
All absent divers can still qualify for the Worlds via discretionary picks.
Former world champion Tom Daley and Olympic gold medallists Chris Mears and Jack Laugher will miss this week's British Championships in Edinburgh with minor injuries.