Chief Constable of Gloucestershire Tony Butler said it would involve a fundamental legal change in the role of the police.
But the Association of Chief Police Officers said Mr Blair's proposals were "interesting", but raised concerns over how they would be enforced.
ACPO president Sir John Evans, chief constable of Devon and Cornwall
Constabulary, said: "There are considerable practical and legal problems we would have to examine very closely before we arrived at a practical scheme".
Chief Constable of Gloucestershire Tony Butler said it would involve a fundamental legal change in the role of the police.
"This would be the first occasion I am aware of where the police move from law enforcement to imposing punishment and then collecting a fine."
Speaking on BBC Radio 4's Today programme, he also criticised the way Mr Blair had made the announcement.
He said: "What I think would have been helpful if consultation had taken place before the announcement. This is something which has just been announced out of the blue."
Shadow home secretary Ann Widdecombe dismissed Mr Blair's suggestion as a "headline-grabbing gimmick" while civil rights campaigners said it went too far.
Liberal Democrat home affairs spokesman Simon Hughes said: "There is a basic principle of justice - if you commit a crime you are punished. But punishing people who are not charged and not found guilty is fundamentally against civil liberties."
Crime summit
Mr Blair told the Global Ethics Foundation in Tubingen, Germany, of the shame he felt at the drunken behaviour of English football supporters during the Euro 2000 tournament.
He said he hoped on-the-spot fines would help cut the problem of late-night drunkenness in towns and cities.
"A thug might think twice about kicking your gate, throwing traffic cones around your street, or hurling abuse into the night sky if he thought he might get picked up by the police, taken to a cashpoint and asked to pay an on-the-spot fine of, for example, £100," he said.
His speech came after Home Secretary Jack Straw called for local authorities to make more use of their powers to crack down on anti-social behaviour.
He went on: "If the police want that power - and I believe they will, and the public will support it - they should get that power."
The prime minister said he would raise the issue with senior police officers attending a crime summit in Downing Street on Monday.
Spelling out his own personal feelings about crime, Mr Blair said: "On crime, I have no hesitation about being very hard on it.
Mr Blair told his audience: "Bizarrely, as the law stands, the police have the power in Britain to levy on-the-spot fines for cycling on pavements and dog fouling.
"And yet they have to deal with drunks who get offensive and loutish and often can do nothing about it without a long, expensive process through the police station, the courts and beyond."
But barrister and civil rights campaigner Michael Mansfield QC said he was "very concerned" at the idea.
Judge and jury
"What you are actually asking the police force to do is to monitor social behaviour - it is Orwellian in its concept.
"What is going to constitute anti-social behaviour? How is a bobby on the beat going to weigh up whether it's one traffic cone or two traffic cones [being thrown] ... the whole thing is a nonsense."
John Wadham, director of civil rights group Liberty, said there was a danger of penalising the wrong people when police officers were asked to act as "judge and jury", especially in crowd situations.
The National Association of Probation Officers said it would breach European human rights laws on two grounds and place police officers in an impossible position.
"It is unlikely to work because their is no guarantee these thugs are going to have £100 on them anyway," spokesman Harry Fletcher added.
And Norman Brennan, of the Victims of Crime Trust, said: "This is an absolutely ridiculous idea. It is simply the wrong way to deal with criminals."