Since mid-May, members of the public have been advised to wear coverings in enclosed public spaces, where they may encounter people they would not usually meet.
Mask-wearing has been compulsory on public transport in England and at NHS facilities across the UK since 15 June.
Children under 11 and those with certain disabilities will be exempt.
The list of exemptions has not yet been published, but the rules for face masks on public transportexempt anyone who cannot wear one “because of any physical or mental illness or impairment, or disability”, who would experience “severe distress” from doing so, or relies on lip reading, among other reasons.
Mr Hancock told the Commons: “Sadly, sales assistants, cashiers and security guards have suffered disproportionately in this crisis.
“The death rate of sales and retail assistants is 75% higher amongst men and 60% higher amongst women than in the general population.”
He added: “There is also evidence that face coverings increase confidence in people to shop.”
The new rule will not apply to retail staff.
It comes as the UK recorded the deaths of a further 138 people who had tested positive for coronavirus.
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Tory MP Desmond Swayne described the rule as a “monstrous imposition” that would make him less likely to go shopping.
Labour said ministers had been “slow and muddled” on face coverings and questioned why the new rules would not come into force for 11 days.
But Environment Secretary George Eustice told the BBC that research on the use of face coverings, including advice from the World Health Organization, had been “evolving”.
And he said the delay between the announcement and the rule coming into force on 24 July “gives people time to prepare”.
Wearing face coverings in shops is an “appropriate mitigation” against the “overall risk” of the coronavirus, but the rule would not work in pubs, cafes or restaurants, he added.
The latest rules for shops will be enforced by the police, with anyone disregarding them at risk of a fine of up to £100. This will be reduced to £50 if the fine is paid within 14 days.
“A shop can refuse them entry and can call the police if they refuse to comply,” Mr Hancock said.
Martin Hewitt, chair of the National Police Chiefs’ Council, said police should be involved only as a “last resort”.
— bbc news