President Mohamed Ould Abdel Aziz had called the August 5 referendum to push through changes defeated in the Senate in March, but faced protest from opposition and civil society groups as well as the majority of senators.
Mohamed Ould Ghadde spearheaded efforts in the senate including a sit-in against the constitutional changes, but they were approved by 85% of voters in the referendum.
Then on Friday Ghaddes was arrested "at his house in the early hours of the morning by two plainclothes policemen," a police source said.
There was no official statement on the reasons for his arrest.
Two days before the vote Ghadde had been accused by the president of asking for money on WhatsApp from a contact believed to be a businessman living in Morocco, in recordings allegedly intercepted by the security services.
A family member told AFP the police had already "taken his identity card and driving licence and ordered him not to leave the country" on Thursday when he tried to leave for medical treatment in neighbouring Senegal.
Aziz had also said during campaigning that the Senate "costs a lot, has no use and does nothing", and vowed to launch legal action against several senators.