John Apter, who represents rank-and-file officers in England and Wales, has called on businesses to help educate people on the new regulations as a joint effort.
The police chief said forces are now busier than they were before the pandemic and will only respond to a call from a shop if a person is refusing to leave or becomes aggressive.
He told BBC Breakfast: “I think the unfortunate thing is there’s an expectation that the police are almost the first port of call when it comes to enforcement or dealing with, in this case, the face coverings.
“First of all, we just don’t have the capacity, we simply can’t do it, not to the level some people expect which is for us to be almost in every high street, in every store, ensuring that people are wearing a face covering.
The chair of the Police Federation has warned police “just don’t have the capacity” to enforce new face mask rules which came into effect today.
“The retailers and those who operate in these stores or businesses also have a responsibility to educate the public because this is all very new and some people are scared, some people genuinely don’t know what’s expected of them so it’s about a combined effort in educating people.”
People who refuse to wear a mask covering their face and nose in places set out by the government, including supermarkets, shops, takeaways, banks and post offices, could face a £100 fine for today.
However Mr Apter said “enforcement will be absolutely the last resort”.
He added: “If certain customers, and I genuinely believe this will be a tiny minority, if somebody is refusing to leave the store or becomes aggressive of course that’s right that the police should be called.
“But if somebody calls the police because somebody is just not wearing a face covering, I’m afraid that will go into the pot of jobs that my colleagues have to respond to because business as usual is still there – in fact we are now busier than we were before this pandemic – so we have very little capacity.
“So I just want to manage the public’s expectation.”