The police said that the man was arrested on Monday on "suspicion of racially aggravated malicious communications" and that he was later released on bail.
The case is among "a number of ongoing investigations by the police into a number of serious abusive and threatening letters, emails and telephone calls," Miller said.
Miller, a 51-year-old investment banker, was the chief claimant in a case that thwarted the UK government's plans to formally begin the process of Britain's exit from the European Union without a vote in parliament. British Prime Minister Theresa May had hoped to bypass MPs to trigger Article 50 of the Lisbon Treaty -- the legal mechanism required to begin the divorce process from the union -- by the end of March.
Rape and death threats
Following the court decision, Miller -- who was born in Guyana but has lived in the UK for 41 years -- says online trolls sent her rape and death threats.
She said other abuse included people telling her she was not human, that she was a primate, and that she belonged in a kitchen.
"That's the nicest of some of them. It is unbelievable," Miller said.
"I am really cross at the politicians and the media who are whipping this up because they are the ones inciting racism and violence and acrimony."
Britain voted in a referendum in June to leave the EU following months of public debate that was punctuated by divisiveness and seen to have fueled an increase in racial hate attacks.
Supreme Court hears government appeal
Britain's High Court ruled November 3
that triggering Article 50 would need to go through parliament, and a government appeal to that decision
is now being heard by the Supreme Court.
All 11 Supreme Court judges will hear the four-day case -- the first time this has happened since the court was established in 2009 -- before giving their ruling in early 2017.
Experts say parliament is unlikely to block Brexit outright, but the deliberations mean a Brexit could be delayed, particularly by opposition in the upper chamber, the House of Lords. Lawmakers may get a chance to influence what kind of deal the government negotiates with the EU.
May appeared optimistic about a clean Brexit, saying Tuesday that she was looking for a "red, white and blue Brexit," referring to the colors of Britain's flag, that is "the right deal for Britain."
The EU's chief Brexit negotiator, Michel Barnier, warned Tuesday that Britain may only have 18 months to strike an exit deal
from the bloc.