Care home workers must be doubly vaccinated to continue in their roles as of last month.
The ruling, brought in by Government to protect vulnerable residents of care homes, has led to fears of a national exodus of up to 50,000 staff.
Some 11 care home staff employed by North Yorkshire County Council chose to leave their roles rather than be vaccinated.
Five of the 11 worked in Harrogate, leaving a gap in services.
“Unfortunately five of those were in the Harrogate area and that has caused some issues for us.
“We’re obviously trying to replace people who have left us and that means we’ve had to temporarily downscale some day and respite services.”
Private social care settings in North Yorkshire have seen 220 people leave due their vaccine status, Mr Webb said.
A campaign to urgently recruit more care workers in the region has seen 170 applicatons, Mr Webb confirmed.
The Make Care Matter campaign was launched last month, and Mr Webb said that 31 interviews were scheduled with 14 people already in post.