Brar, 78, on a private visit, was returning to his hotel with his wife when he was attacked in central London by four men on September 30 and suffered a wound on his neck and cheek.
A 36-year-old man was arrested in west London on Wednesday on suspicion of conspiracy to murder and inflicting grievous bodily harm with intent, while a 55-year-old woman was arrested on suspicion of assisting an offender.
The man is in custody at a police station in central London. The woman has been bailed on condition of having to return on a future date pending further inquiries.
Barjinder Singh Sangha, 33, of Wolverhampton and Mandeep Singh Sandhu, 34, of Great Barr, Birmingham, have already been charged with intent to do grievous bodily harm on Brar and had appeared in custody at Westminster Magistrates' Court on October 8.
Sangha was also charged with "common assault" on Brar's wife, Meena.
The two Indian-origin men are to appear before a UK Court here for the next hearing on December 7.
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"Whether they will plead guilty or not will be known on that day," a spokeswoman of the Metropolitan Police had said.
Brar had said after the attack that he was convinced it was an attempt to assassinate him by "pro-Khalistan elements" for his role in the 1984 "Operation Bluestar" that was aimed at flushing out Sikh militants led by Jarnail Singh Bhindrawale from the Golden Temple in Amritsar.
A decorated soldier, Brar saw action in the 1971 war with Pakistan, and was among the first to enter Dhaka when the Indian army forced Pakistani army into surrender.