The 50-year-old man was detained in west London on Wednesday on suspicion of racially aggravated malicious communications. He has been bailed until mid-February.
The arrest follows a complaint made on 6 November relating to online threats.
Eight "cease and desist" notices were issued to individuals across the UK.
The Met Police advise recipients that continuing with their current actions or behaviour could result in police action.
Who is Gina Miller?
The Met said the Crown Prosecution Service advised in December that no further action would be taken against a 55-year-old man from Swindon who was also arrested on suspicion of racially aggravated malicious communications for online threats made to Ms Miller from 3 November onwards.
Ms Miller, a partner in an investment management firm, was the lead claimant in the legal fight to get Parliament to vote on whether the UK can start the process of leaving the EU.
She and her fellow claimants - including hairdresser Deir Dos Santos and the crowd-funded People's Challenge group - won their case at the High Court in November.
On Tuesday the government lost its appeal against the High Court's decision in the Supreme Court.
It means both Houses of Parliament will now have a vote on a bill to invoke Article 50 of the Lisbon Treaty signalling the UK's intention to leave the European Union (EU).
That will start the process of two years of negotiations to redefine the UK's relationship with the EU.
A parliamentary bill paving the way for talks with the EU could be introduced as early as Thursday.
A man arrested over alleged threats made against Gina Miller - the woman behind the Brexit legal challenge - has been released on bail.