Mr Connell, a solicitor and chief executive adviser to the Convention of Scottish Local Authorities, was appointed to the council following reorganisation. He had previously worked at Grampian RC.
A council statement said: 'The chief executive has been suspended by the council pending investigation due to an internal administrative matter. No further details will be given at this time.'
A spokeswoman refused to say if the investigation was linked to allegations first aired last year that members of the ruling SNP group were guilty of a gross abuse of expenses and that an internal inquiry was a whitewash.
Mr Connell's suspension is the latest in a series of breakdowns in relations between Scottish chief executives and their political leadership.
Inverclyde chief executive Graeme Bettison left the council last November after falling out with the political leaders. City of Glasgow chief executive John Anderson has just been forced out by the new leadership. And West Dunbartonshire chief executive Michael Watters continues his public battle with leader Andy White.