It is understood Paul Davies, the executive director for social care and inclusion, is among them.
Council bosses said "issues" had been raised within social care but remain tight-lipped over the details and would not confirm the suspensions.
Council leader Mike Bird said: "We're taking a look at issues which have been raised with us within social care.
"This work is in hand and may take some time and while this is taking place we can't comment further.
"This work will be fully reported in due course.
"We would never comment on individual employment matters."
Mr Davies joined the council in spring 2010 after moving from Oldham Council, where he had been assistant executive director for adult social care since 2004.
He was in charge of Walsall's social care and inclusion department when a controversial shake-up of domiciliary care charges was introduced.
Under the new charges, brought in from April 2011, people on disability living allowance and attendance allowance are asked to pay towards the services they receive.
The benefits-based charging system was expected to bring in up to £2 million a year for the cash-strapped council.
He was also in charge of the department during a shake-up of meals on wheels services in which pensioners who received them were encouraged to order food from cafes or attend lunch clubs instead.
The shake up of the service was designed to save £1 million over three years.