Eleven men and one woman were detained on suspicion of offences including assaulting police officers, affray and racially aggravated public order, and all remain in custody, police said.
The arrests followed a stand-off at a marina in Gosport on Sunday evening involving about 150 anti-migrant demonstrators, during which flares were set off and scuffles broke out with police. A police cordon was in place on Haslar Road, where officers said the atmosphere at the protest mostly remained peaceful.
Some protesters blocked police vans from advancing by standing in front of them and chanting "shame on you" and "deport the lot".
The Home Office said the migrants, picked up in a mid-Channel rescue operation by the RNLI alongside a French vessel, were taken by coach to a processing centre in Kent.
The landing is the second known arrival of large numbers of migrants this far west along the south coast in recent years, according to the BBC's reporting.