Members of trade union Unison voted for strike action in response to concerns around working conditions at Kirklees Council, which was graded inadequate by Ofsted in November 2016.
At the same time, DCS Sarah Callaghan announced she was leaving the authority despite only being in post since April last year.
Ofsted's report stated that since Callaghan had assumed her post, the council had made "considerable efforts" to accelerate the improvement of children's services.
However, inspectors said many recent developments were yet to be embedded, and that more than 500 children were receiving a poor service, with some "remaining in unsafe environments".
The Department for Education responded by appointing Eleanor Brazil, who has worked with other struggling children's services such as Slough, as commissioner of children's services at the local authority.
However, Unison branch secretary Paul Holmes said social workers are still citing issues including high caseloads, inconsistent support for staff, and poor IT systems.
"People are resigning," Holmes said.
"People leave in droves. Agency workers can turn stuff down and walk away. The permanent workers can't. They feel responsible for something that they feel is unsafe. We don't want any children to be at risk."
Holmes said staff are also frustrated by receiving lower salaries than neighbouring local authorities offer. He added that Callaghan's departure would further destabilise children's services.
"It just increases the uncertainty in the department. Social workers feel completely leaderless and abandoned," he said.
The strike is set to take place on 27 January with Holmes expecting a complete shutdown of services for 24 hours.
Kirklees Council's portfolio holder for family support and child protection Erin Hill has urged staff to talk to her about concerns rather than cause "a lot of disruption".
"While I recognise we still have a way to go, my view is that we are dealing with the issues he raised as well and as quickly as we can, with support from the DfE," she said.
Commenting on Callaghan's departure, Kirklees Council chief executive Adrian Lythgo said she had made her decision "in agreement with the council, to pursue new leadership challenges outside of Kirklees".