A 33-year-old man from Portsmouth was arrested on suspicion of obstructing a highway during recent protests.
Separately, a 16-year-old boy was arrested on suspicion of violent disorder linked to demonstrations at Eastney Marina on Sunday.
Hampshire Police activated new powers under the Crime and Policing Act to prohibit face coverings that conceal identity, with the measures taking effect at 10:00 BST.
Police were deployed to Eastney Marina on 6 September after hundreds of protesters blocked roads, preventing coaches carrying 120 migrants from departing.