Nick Hulme, the boss of the East Suffolk and North Essex Foundation Trust, also warned the public's goodwill through industrial action is now being stretched.
The health service faces a summer of chaos after members of the Royal College of Nursing rejected a pay deal. The union announced members will walk out from 8pm on Sunday April 30 to 8pm on Tuesday May 2, affecting the May Day weekend.
They will refuse to deliver any services, including in A&E and cancer wards.
It comes despite nurses and midwives represented by Unison voting to accept the same pay offer.
There are fears future strikes by RCN members could be co-ordinated with junior doctors, who walked out for four days last week.
Mr Hulme told BBC Radio 4: "If there is a delay to cancer care, there are many people who have been waiting far too long and this will only exacerbate that risk.
"There has been a huge amount of goodwill, and that has been stretched during the action by nurses and junior doctors."
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