Jim McCabe, the Labour leader of North Lanarkshire Council, was taken to Monklands Hospital in Airdrie on Saturday with a suspected heart attack.
Sources within the authority said that had now been ruled out but were unable to say when Mr McCabe would return to work.
The 73-year-old has headed North Lanarkshire since 1998 and is one of the highest profile individuals in Scottish local government. He has been the focus of much attention in recent months about the imposition of the so-called Bedroom Tax.
Labour colleague Jim Smith is interim leader of the council.