This comes after masked demonstrators were seen at anti-migrant protests in Dover and Portsmouth last weekend.
A separate order will also allow officers to require people to remove masks and other items used to conceal their identity.
Activist Danny Thomas, who organised last weekend's protests, said on social media his group Patriot Platform would not attend the planned Portsmouth demonstration.
"No member, organiser, representative, or affiliate of Patriot Platform will attend, speak at, steward, or take part in any event in Portsmouth," he wrote.
Assistant Chief Constable Paul Bartolomeo said: "It is important to stress that this power will apply to any groups that attend the protest and will be enforced equally and impartially.
"Let me be clear, these powers are not being implemented to prevent protest, but they are being used to help prevent crime and disorder, while making communities feel safer."
Staffordshire Police also said it would ban the use of face coverings at a protest in Tamworth on Saturday, where Britain First is planning a so-called March for Remigration.
Northumbria Police has a similar ban in place in Newcastle city centre.