The arrestees are Nurul Amin, Nizam Uddin and Mohamamd Ayas.
Director of Rab Legal and Media Wing, Lieutenant Colonel Ashique Billah, said Rab members arrested them from the area around 2 pm.
He said it has primarily been confirmed that they were involved in the murder.
Rab produced them before a court with a 10-day remand prayer.
Also read: Major Sinha murder: OC Pradeep, Inspector Liakat on 7-day remand
Major (retd) Sinha was killed in police firing at Baharchhara police check-post on July 31.
Sharmin Shahriar Ferdous, elder sister of Sinha, filed a case with Teknaf Senior Judicial Magistrate Court after the incident on August 5.
Also read: 9 sued over killing of ex-Major Sinha in Cox’s Bazar
Senior Judicial Magistrate Tamanna Farah issued warrants for the arrest of all the accused after taking the case into cognizance on that day.
Officer-In-Charge (OC) of Teknaf Police Station Pradeep Kumar Das, an accused in the murder case, surrendered the following day and police later took him to Cox’s Bazar.
Also read: OC Pradeep, 6 others suspended over Sinha murder
The Home Ministry formed a four-member committee, headed by Mizanur Rahman, additional divisional commissioner (development), on August 2.
The authorities on August 2 suspended 21 police officials, including the in-charge of Baharchhara police outpost, in connection with the killing.
Also read: 21 cops suspended over killing of ex-Army major in Teknaf
Prime Minister Sheikh Hasina on August 4 assured the mother of Major Sinha of proper investigation into the murder of her son and the trial of his killers.
Also read: PM assures ex-Major Sinha's mother of fair trial of his murder