From 29 March it will become illegal to nurse any that are injured and return them to the wild.
Rescue groups have warned that they and vets will be forced to euthanise animals, prompting anger from wildlife lovers, with more than 37,000 signing a petition against the new rules.
Non-native grey squirrels are blamed for the decline in native reds by competing for food and infecting them with the squirrel pox virus.
Natural England has told rescuers that the Invasive Alien Species Order 2019 means no more licences for the species will be issued, leaving them unable to help if a member of the public finds an injured one.
EU regulations, devised in 2014, aimed at controlling non-native species that put natural plants and wildlife at risk, are taking effect in EU countries at different times.
But animal lovers have written to environment secretary Michael Gove expressing their “shock and horror”.
“To so harshly interpret EU legislation so that the most vulnerable minority of these already vilified species (orphaned and injured) are robbed of the chance of rescue seems utterly heartless,” the letter says.
Natalia Doran, from rescue group Urban Squirrels, said: “While Urban Squirrels can guarantee that it will abide by the law, we have to warn that a lot of ‘civil disobedience’ rescue will take place and the order will be in reality unenforceable.”
She suggested grey squirrels could be controlled with an oral contraceptive.
“The numbers of grey squirrels that come into rescue are not significant statistically but are very significant for the compassion footprint of humanity,” she said.
Jade Emery, of Animal Aid, said: “This tyrannical and pointless regulation will mean rescue organisations are forbidden from helping a single squirrel.”
A Defra spokesperson said: “With only an estimated 15,000 red squirrels left in England, it is crucial we work to protect this endangered species.
“Invasive non-native species, including the grey squirrel, challenge the survival of our rarest species and damage sensitive ecosystems.
“Their impacts are severe and growing, costing the economy more than £1.7bn per year.”
The Forestry Commission says grey squirrels strip bark from trees, causing up to £10m of damage each year.
Environment department chiefs are helping fund research on contraceptives for grey squirrels.
Muntjacs are blamed for clearing growth that supports native birds and butterflies.