The provisions are contained in the Police and Justice Bill. It gives police the power to delegate responsibility for fining offenders to other authority figures, potentially teachers and council staff.
Union leaders said this would put teachers at "risk of physical abuse" and they would not relish being turned into "quasi-police".
The Home Office said it has no plans yet to extend the powers beyond trading standards officers.
Chris Keates, the general secretary of NASUWT, said: "It's inappropriate for teachers to issue fines. They have no backing to enforce them and it could put them at risk of reprisal.
"Putting heads and teachers in the role of quasi-police would undoubtedly change the nature of the relationship between staff and students."
The National Union of Teachers said the move would sow the seeds of conflict and antagonism.
"Schools don't want to be judge and jury - that's a role for the courts," a spokeswoman said. "Teachers already have the ability to punish pupils, but here you're talking about a different level. We need to be able to co-operate with pupils and parents."
A Professional Association of Teachers spokesman said it could "put teachers at risk of verbal and physical assault".
"I'm sure most teachers and heads would be very reluctant to get involved in such a scheme, in the same way I suspect most police officers would be reluctant to start helping children with their homework," he said.
While there are no immediate plans to include teachers, the scheme could be extended without separate legislation. It is seen by advocates as a means of lightening police workloads, freeing them to deal with more serious crimes.
On-the-spot fining was introduced in 2001 as part of the Government's drive to crack down on antisocial behaviour. Fines from pound;50 to pound;100 are issued for theft, petty vandalism, drunkenness and littering.
The scheme has had a generally positive reception for cracking down on offenders while unclogging the criminal justice system.