A spokesman for the Western General said he was in the hospital's intensive care unit on a life support machine.
The 63-year-old Labour politician was taken to hospital after slipping and falling outside his official residence in Edinburgh.
He underwent a brain scan at Edinburgh Royal Infirmary and was later transferred by ambulance to the city's Western General Infirmary, which has a neurological unit.
The accident happened less than two months after Mr Dewar returned to work following major heart surgery.
A spokesman for the Western General said he was in the hospital's intensive care unit on a life support machine.
No further statement is planned until Wednesday morning unless there are serious developments overnight.
A Downing Street spokeswoman said Prime Minister Tony Blair was being kept informed of Mr Dewar's condition.
The first minister slipped and fell on the pavement while going to his official car in Edinburgh on Tuesday morning.
He was able to carry out a lunchtime engagement, but three hours after his fall, he felt unwell.
Brain scan
Mr Dewar was seen by Colin Currie, who is medically qualified and a special adviser to Health Minister Susan Deacon.
An ambulance was sent after Dr Currie consulted with accident and emergency consultant Colin Robertson and explained to him what had happened.
He was taken to Edinburgh Royal Infirmary for tests, including a Cat scan.
"As a result of what they found in the Cat scan we are now transferring him to the Western General," said Mr Whitton.
It was not clear if surgery was required.
"What seems to have happened is that in the fall, although he did not bump his head, he may have damaged a blood vessel in his head, as a result of which he is suffering bleeding to the head," said Mr Whitton.
Mr Dewar only returned to work on 14 August, less than four months after undergoing major heart surgery.
Consultants' warning
He had the surgery in May during which a faulty heart valve was replaced during a four-hour operation.
Mr Dewar, a bachelor, received the mechanical valve after a routine check-up revealed heart "irregularities".
Consultants warned Mr Dewar that his recovery would take several months and require him to take regular exercise, forcing him to take to the streets of his Glasgow Anniesland constituency for long walks.
There was speculation during his absence that the illness would prevent him making a comeback on the political stage but the veteran politician was determined to continue the job of leading the government in Scotland.
The post of first minister was created after devolution in May 1999. Prior to that, Mr Dewar was secretary of state for Scotland, a role which carried a much higher-profile than it has now.
Liberal Democrat Deputy First Minister, Jim Wallace, took on Mr Dewar's responsibilities during his absence.
A spokesman for the executive said it was likely Mr Wallace would step in again "if necessary".
Scottish National Party leader John Swinney said he hoped Mr Dewar would make a swift recovery.
Scottish Secretary John Reid told the BBC's Newsnight programme that Mr Dewar was the driving force behind the creation of the Scottish Parliament.
"Donald made his name in United Kingdom politics but he is unparalleled in Scottish politics, not just among those who support the Labour Party but people of all political persuasions.
'Very serious'
"So many people will be pressing their fingers together, crossing them very tightly, and hoping and praying Donald will be able to battle his way through this but I can't overestimate to you how serious the situation is.
"It is very, very serious indeed."
Mr Dewar's daughter Marion, who lives in Brussels, and son Ian have been contacted and on Tuesday night were heading to Edinburgh.
After his heart operation and during his recuperation Mr Dewar kept a close eye on proceedings in the Scottish Parliament.
In July, he ordered Tom McCabe, the Minister for Parliament, to deliver a stern warning to his Labour colleagues on the Scottish Executive.
Mr Dewar told them to stop squabbling - or face the sack, after a row broke out between Finance Minister Jack McConnell and Susan Deacon over £34m of unspent health cash.