Cheshire East Council said the suspension of chief executive Mike Suarez after a disciplinary committee meeting on Monday was a "neutral act".
The Conservative-run authority will not reveal details of the allegations.
Councillor Howard Murray said the suspension was "a neutral act taken in the interests of both the council and chief executive".
The chair of the investigation and disciplinary committee added: "It is important that this investigation is undertaken objectively and therefore it would be inappropriate to make any further comment at this stage."

19 July 2016 Last updated at 12:42 BST
A heatwave in Spain and a strong breeze could be bringing the hot weather north to the UK. This is called a Spanish plume.
This could also mean hot and humid storms later this week.
We spoke to our resident weather expert Simon King to find out more...
A council boss has been suspended while an independent investigation into his conduct takes place.
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Glorious sunshine and temperatures of up to 35 degrees in parts of the UK, but what is causing it?